text:
Teenage Mutant Ninja Turtles
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article is about the franchise. For entries in the franchise, see Teenage Mutant Ninja Turtles (disambiguation).
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (May 2016) (Learn how and when to remove this template message)
Teenage Mutant Ninja Turtles
Art by Kevin Eastman
Publication information
Publisher
Mirage Studios[1]
First appearance
Teenage Mutant Ninja Turtles #1 (May 1984)
Created by
Kevin Eastman
Peter Laird
In-story information
Base(s)
Manhattan, New York City
Member(s)
Leonardo
Donatello
Michelangelo
Raphael
The Teenage Mutant Ninja Turtles (often shortened to TMNT or Ninja Turtles) are four fictional teenaged anthropomorphic turtles named after Renaissance Italian artists. They were trained by their anthropomorphic rat sensei in the art of ninjutsu. From their home in sewers of New York City, they battle petty criminals, evil overlords, mutated creatures, and alien invaders while attempting to remain hidden from society. They were created by Kevin Eastman and Peter Laird.
The characters originated in comic books published by Mirage Studios and expanded into cartoon series, films, video games, toys, and other merchandise.[2] During the peak of the franchise's popularity in the late 1980s and early 1990s, it gained worldwide success and fame.
Contents
[hide]
1 History
2 Main characters
3 Comics
3.1 Mirage
3.2 Teenage Mutant Ninja Turtles Adventures
3.3 Dreamwave
3.4 IDW
3.5 Manga
3.6 Comic strip
4 Television series
4.1 First animated series (1987–1996)
4.2 Original video animation
4.3 Live-action series (1997–1998)
4.4 Second animated series (2003–2009)
4.5 Third animated series (2012–2017)
4.6 Fourth animated series (2018)
5 Feature films
6 Merchandise
6.1 Toys
7 Video games
8 In other media
8.1 Tabletop role playing game
8.2 Food tie-ins
8.3 Concert tour
8.4 At the Disney-MGM Studios theme park
9 Parodies
10 Controversies
10.1 Departure from origins
10.2 Teenage Mutant "Hero" Turtles
11 Ownership rights
11.1 Television
11.2 Films
11.3 Comic books
12 See also
13 References
14 Bibliography
15 External links
History[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2015) (Learn how and when to remove this template message)
Cover of Teenage Mutant Ninja Turtles #1 (May 1984)
The Teenage Mutant Ninja Turtles first appeared in an American comic book published by Mirage Studios in 1984 in Dover, New Hampshire. The concept arose from a humorous drawing sketched out by Eastman during a casual evening of brainstorming and bad television with Laird.[3] Using money from a tax refund, together with a loan from Eastman’s uncle, the young artists self-published a single-issue comic intended to parody four of the most popular comics of the early 1980s: Marvel Comics’ Daredevil and New Mutants, Dave Sim’s Cerebus, and Frank Miller’s Ronin.[4] The TMNT comic book series has been published in various incarnations by various comic book companies since 1984.
The Turtles started their rise to mainstream success when a licensing agent, Mark Freedman, sought out Eastman and Laird to propose wider merchandising opportunities for the franchise. In 1986, Dark Horse Miniatures produced a set of 15-mm (approximately 0.6 inch) lead figurines. In January 1987, Eastman and Laird visited the offices of Playmates Toys, a small California toy company that wanted to expand into the action-figure market. Development was undertaken by a creative team of companies and individuals: Jerry Sachs, advertising agent of Sachs-Finley Agency, brought together the animators at Murakami-Wolf-Swenson headed by Fred Wolf. Wolf and his team combined concepts and ideas with the Playmates marketing crew, headed by Karl Aaronian, vice president (VP) of sales Richard Sallis, and VP of Playmates Bill Carlson.[5]
Aaronian brought on several designers and concepteur and writer John C. Schulte, and worked out the simple backstory that would live on toy packaging for the entire run of the product and show.[5] Sachs called the high concept pitch "Green Against Brick". The sense of humor was honed with the collaboration of the Murakami-Wolf-Swenson animation firm's writers. Playmates and their team essentially served as associate producers and contributing writers to the miniseries that was first launched to sell-in the toy action figures. Phrases like "Heroes in a half shell" and many of the comical catch phrases and battle cries ("Turtle power!") came from the writing and conceptualization of this creative team. As the series developed, veteran writer Jack Mendelsohn came on board as both a story editor and scriptwriter. David Wise, Michael Charles Hill, and Michael Reaves wrote most of the scripts.
The miniseries was repeated three times before it found an audience.[clarification needed] Once the product started selling, the show got syndicated and picked up and backed by Group W, which funded the next round of animation. The show then went network, on CBS. Accompanied by the popular Teenage Mutant Ninja Turtles 1987 TV series, and the subsequent action figure line, Teenage Mutant Ninja Turtles became a mainstream success. At the height of the frenzy, in the late 1980s and early 1990s, the Turtles' likenesses could be found on a wide range of children's merchandise, from Pez dispensers to skateboards, breakfast cereal, video games, school supplies, linens, towels, cameras, and toy shaving kits.
While the animated TV series, which lasted for 10 seasons until 1996, was more light-hearted, the comic-book series continued in a much darker and grittier tone. In 1990, a live-action feature film was released, with the Turtles and Splinter being portrayed by actors in partially animatronic suits created by Jim Henson's Creature Shop. The film became one of the most successful independent films and spawned two sequels, as well as inspiring a three-dimensional animated film set in the same continuity, which was released in 2007 under the title TMNT. After the end of the cartoon series, a live-action series in the vein of the films was created in 1997 in conjunction with Saban Entertainment. The series was called Ninja Turtles: The Next Mutation and introduced a fifth, female turtle called Venus de Milo. However, the series was largely unsuccessful and was canceled after one season.
The property lay dormant until 2003, when a new animated TV series also entitled Teenage Mutant Ninja Turtles began to air on Fox Box (4Kids TV). The series storyline stuck much closer to the original Mirage comic book series, but was still less violent. It lasted for seven seasons and 156 episodes, ending in February 2009.
On October 21, 2009, it was announced that cable channel Nickelodeon (a subsidiary of Viacom) had purchased all of Mirage's rights to the Teenage Mutant Ninja Turtles property. Mirage retains the rights to publish 18 issues a year, though the future involvement of Mirage with the Turtles and the future of Mirage Studios itself is unknown.[6] Nickelodeon has developed a new CGI-animated TMNT television series and partnered with fellow Viacom company Paramount Pictures to bring a new TMNT movie to theaters. The TV show premiered on Nickelodeon on September 29, 2012.[7] The live-action film, produced by Platinum Dunes, Nickelodeon Movies, and Paramount Pictures, directed by Jonathan Liebesman, and produced by Michael Bay, was released on August 8, 2014.[8]
Main characters[edit]
Main article: List of Teenage Mutant Ninja Turtles characters
Leonardo (Leo) – The tactical, courageous leader and devoted student of his sensei, Leonardo wears a blue mask and wields two katana. As the most conscientious of the four, he often bears the burden of responsibility for his brothers, which commonly leads to conflict with Raphael. Leonardo was named after the Italian polymath, painter, engineer, inventor, writer, anatomist, and sculptor, Leonardo da Vinci.
Raphael (Raph) – The team's bad boy, Raphael wears a red mask and wields a pair of sai. He is physically very strong, has an aggressive nature, and seldom hesitates to throw the first punch. He is often depicted with a very pronounced New York accent. His personality can be fierce and sarcastic, and oftentimes delivers deadpan humor. He is intensely loyal to his brothers and sensei. He is named after the Italian painter and architect of the High Renaissance, Raphael.[9]
Donatello (Donnie or Don) – The scientist, inventor, engineer, and technological genius, Donatello wears a purple mask and wields a bo staff. Donatello is perhaps the least violent turtle, preferring to use his knowledge to solve conflicts, but never hesitates to defend his brothers. He is named after the early Renaissance Italian artist and sculptor from Florence, Donatello.
Michelangelo (Mikey) – The most stereotypical teenager of the team, Michelangelo is a free-spirited, relaxed, and often goofy jokester, and known for his love of pizza. Michelangelo wears an orange mask and wields a pair of nunchucks. He provides the comic relief, though he still has an adventurous side. The least mature of the four Turtles, he shows characteristics of a "surfer" type and is often depicted with a Southern Californian accent. He is named after the Italian Renaissance painter, sculptor, architect, poet, and engineer, Michelangelo. His name was originally misspelled "Michaelangelo" by Peter Laird and Kevin Eastman.[9]
Splinter – The Turtles' sensei and adoptive father, Splinter is a Japanese mutant rat that learned the ways of ninjutsu from his owner and master, Hamato Yoshi. In the 1987 TV series, Archie Comics series, and the 2012 TV series, Splinter was Hamato Yoshi mutated into a humanoid rat. In the 2003 TV series, he was Hamato Yoshi's pet rat. He was mutated from a mysterious ooze from the TCRI building. In the IDW comics, he is Hamato Yoshi reincarnated as a mutated rat.
April O'Neil – A former lab assistant to the mad scientist Baxter Stockman, April is the plucky human companion of the Turtles. April first met the Turtles when they saved her from Baxter's Mouser robots. She embarks on many of the Turtles' adventures and aids them by doing the work in public that the Turtles cannot. In the 1987 TV series, Archie Comics series, the subsequent three films, and the 2014 film reboot, April was a television news reporter. In the 2007 CGI film (following the continuity from the original three films), Casey Jones and she work for a shipping firm. In the 2012 series, April is a teenager who is rescued by the TMNTs and later given some "crash courses" in being a ninja by Splinter.
Casey Jones – A vigilante who wears a hockey mask to protect his identity, Casey Jones has become one of the Turtles' closest allies, as well as a love interest to April. Casey first encountered the Turtles after having a fight with Raphael. He fights crime with an assortment of sporting goods he carries in a golf bag, such as baseball bats, golf clubs, and hockey sticks.
The Shredder – A villainous ninjutsu master called Oroku Saki, he is the leader of the Foot Clan, an evil ninja clan. In every incarnation of the TMNT franchise, he has been the archenemy of Splinter and the Turtles. The Shredder prefers to use his armor instead of weapons in some versions.
Foot Soldiers/Ninjas – The ninjas of the Foot Clan, working for the Shredder.
Karai – A female high-rank member of the Foot Clan, she has appeared in several different TMNT comics, cartoons, and films, as well as in multiple video games. In some incarnations of the character, she is closely related to Shredder as his adopted daughter or biological granddaughter. In most works, she shares an ambiguous rivalry with Leonardo, which occasionally even borders on romantic interest.
Comics[edit]
Mirage[edit]
Main article: Teenage Mutant Ninja Turtles (Mirage Studios)
Eastman and Laird's Teenage Mutant Ninja Turtles premiered in May 1984, at a comic book convention held at a local Sheraton Hotel in Portsmouth, New Hampshire. It was published by Mirage Studios in an oversized magazine-style format using black and white artwork on cheap newsprint, limited to a print run of only 3,250 copies.[10] Through a clever media kit that included a press release in Comic Buyer's Guide #542 and a full-page ad placed in Comic Buyer's Guide #547, the public's interest was piqued and thus began the Turtle phenomenon. The small print runs made these early comics and trade magazines instant collector items, and within months, they were trading for over 50 times their cover price. The name "Mirage Studios" was chosen because of Eastman and Laird's lack of a professional art studio at the start of their career, before their creation made them both multimillionaires.
Mirage also published a bimonthly companion book entitled Tales of the Teenage Mutant Ninja Turtles, featuring art by Ryan Brown and Jim Lawson, which was designed to fill in the gaps of continuity in the TMNT universe. This put the original series and Tales in the same mainstream continuity, and the two are thus canon to each other. The title's first volume was from 1987–1989, released in alternating months with the regular Eastman and Laird book. All seven issues of volume one have been collected in trade paperback form twice, and 25 issues of volume two have been collected in trades of five issues each.
As the TMNT phenomenon proliferated to other media, Eastman and Laird found themselves administrating an international merchandising juggernaut. However, this prevented the two creators from participating in the day-to-day work of writing and illustrating a monthly comic book. So, many guest artists were invited to showcase their unique talents in the TMNT universe. The breadth of diversity found in the various short stories gave the series a disjointed, anthology-like feel. Fans stuck with the series, and what was originally intended as a one-shot became a continuing series that lasted for 129 issues, spanning four separate volumes (having 62, 13, 23, and 32 issues in the four distinct volumes).
In June 1996, Image Comics took over publishing the title in what is considered "volume 3" of the series. It was a slightly more action-oriented TMNT series and although notable for inflicting major physical changes on the main characters, Peter Laird, co-creator of the TMNT, has said this volume is no longer in canon as he began publishing volume 4 at Mirage Publishing. As an explanation, he offered in the pages of the volume 4 (issue #8) letter column: "It just didn't feel right." [11]
After taking back the series from Image Comics, Mirage Studios resumed publication of a fourth volume in December 2001, under the simple title TMNT. After the publication of issue number 28, writer Peter Laird placed the series on an eight-month hiatus to devote himself to production of the 2007 TMNT movie. However, after that eight months had passed, Mirage's official website went on to list the series as in "indefinite hiatus". In January 2008, Mirage had finally confirmed that the series would return in May 2008. Issues 29 and 30 had a limited printing of 1,000 copies each, and were available through the official TMNT website. Although the purchase agreement with Nickelodeon allows Laird to produce up to 18 comics a year set in the original Mirage continuity, no new material was released in the next few years. The latest issue of TMNT volume 4 was issue #32 which came out in print May 4, 2014, and online on May 9, 2014, almost 4 years after issue #31 was last released.
Teenage Mutant Ninja Turtles Adventures[edit]
Main article: Teenage Mutant Ninja Turtles Adventures
Teenage Mutant Ninja Turtles Adventures was a comic-book series published from August 1988 to October 1995 by Archie Comics. The initial storylines were close adaptations of the 1987 TV series, but with the fifth issue, Eastman and Laird decided to hand the series over to Mirage Studios employees Ryan Brown and Stephen Murphy, who immediately abandoned the animated series adaptations and took the title in a decidedly different direction with all-new original adventures, including the uniting of several of the series' recurring characters as a separate team, the Mighty Mutanimals.
Dreamwave[edit]
Main article: Teenage Mutant Ninja Turtles (Dreamwave Productions)
A monthly comic inspired by the 2003 TV series was published by Dreamwave Productions from June to December 2003. It was written by Peter David and illustrated by LeSean Thomas. In the first four issues, which were the only ones directly adapted from the TV series, the story was told from the perspectives of April, Baxter, Casey, and a pair of New York City police officers.
IDW[edit]
Main article: Teenage Mutant Ninja Turtles (IDW Publishing)
In April 2011, IDW Publishing announced that they had acquired the license to publish new collections of Mirage storylines and a new ongoing series.[12] The first issue of the new series was released on August 24, 2011. Turtles co-creator Kevin Eastman and Tom Waltz write, with Eastman and Dan Duncan handling art chores.
Manga[edit]
The Turtles have appeared in several manga series.
Mutant Turtles (ミュータント・タートルズ, Myūtanto Tātoruzu) is a 15-issue series by Tsutomu Oyamada, Zuki mora, and Yoshimi Hamada that simply adapted episodes of the original American animated series.
Super Turtles (スーパータートルズ Sūpā Tātoruzu) is a three-issue miniseries by Hidemasa Idemitsu, Tetsurō Kawade, and Toshio Kudō that featured the "TMNT Supermutants" Turtle toys that were on sale at the time. The first volume of the anime miniseries followed this storyline.
Mutant Turtles Gaiden (ミュータント・タートルズ外伝, Myūtanto Tātoruzu Gaiden) by Hiroshi Kanno is a reinterpretation of the Turtles story with no connection to the previous manga.
Mutant Turtles III (ミュータント・タートルズ３, Myūtanto Tātoruzu Tsuri) is Yasuhiko Hachino's adaptation of the third feature film.
Mutant Turtles '95 (ミュータント・タートルズ９５, Myūtanto Tātoruzu Kyūjūgo) is a 1995 series by Ogata Nobu which ran in Comic BomBom.
Mutant Turtles '96 (ミュータント・タートルズ９６, Myūtanto Tātoruzu Kyūjūroku) is a continuation of the 1995 series when it continued to run through 1996.
Comic strip[edit]
Main article: Teenage Mutant Ninja Turtles (comic strip)
A daily comic strip written and illustrated by Dan Berger began in 1990. It featured an adventure story Monday through Friday and activity puzzles on weekends (with fan art appearing later). The comic strip was published in syndication until its cancellation in December 1996. At its highest point in popularity, it was published in over 250 newspapers.
Television series[edit]
First animated series (1987–1996)[edit]
Main article: Teenage Mutant Ninja Turtles (1987 TV series)
Logo of the 1987 cartoon
When little-known Playmates Toys, Inc. was approached about producing a TMNTs action figure line, they were cautious of the risk and requested that a television deal be acquired first.[13][14] On December 28, 1987, the TMNT's first cartoon series began, starting as a five-part miniseries and becoming a regular Saturday-morning syndicated series on October 1, 1988, with 13 more episodes. The series was produced by Murakami-Wolf-Swenson Film Productions, Inc. (later Fred Wolf Films). Mirage Studios does not own the rights to this cartoon series. The show places a much stronger emphasis on humor than the comics do. Here, the Ninja Turtles are portrayed as four wise-cracking, pizza-obsessed superheroes that fight the forces of evil from their sewer hideout, and they make their first appearance in masks color-coded to each turtle, where previously they had all worn red.[15]
The cast included new and different characters, such as Bebop and Rocksteady and the Neutrinos. Original characters such as Splinter, Shredder, and the Foot Soldiers stayed true to the comics in appearance and alignment only. Instead of being Hamato Yoshi's mutated pet rat, Splinter was a mutated Hamato himself. The Foot Soldiers changed from human ninjas to an endless supply of robotic grunts, allowing large numbers of them to be destroyed without anyone dying (this was a very important decision in terms of the show's child audience; excessive violence would have alienated parents of children, the show's target demographic). Krang, one of the series' most memorable villains, was inspired by the design of the Utrom, a benign alien race from the Mirage comics. The animated Krang, however, was instead an evil warlord from Dimension X. Baxter Stockman, whose race was changed from black to white either due to apprehension toward depicting a villainous African American character in a children's cartoon or that for Shredder to boss around a black Stockman would be perceived as racist. Either way, Stockman was rewritten as a shy and meek lackey to Shredder, later mutating into an anthropomorphic housefly. During the final two seasons of the show, to combat the rising popularity of Mighty Morphin Power Rangers, the lead villain switched to Lord Dregg, an evil alien overlord bent on world conquest by trying to distract the public into believing that the Turtles were the enemy instead of himself.
Starting on September 25, 1989, the series was expanded to weekdays and it had 47 more episodes for the new season. There were 28 new syndicated episodes for season 4 and only 13 of those episodes aired in 1990. The "European Vacation" episodes were not seen in the United States until USA Network started showing reruns in late 1993 and the "Awesome Easter" episodes were not seen until 1991. These episodes were delayed because of animation or scheduling problems.[16] The turtles are also well known for their use of idiomatic expressions characteristic of the surfer lingo of the time, especially by Michelangelo. Words and phrases included "bummer", "dude", "bogus", "radical", "far-out", "tubuloso", "bodacious", and possibly the most recognized, "cowabunga".[17] On April 21, 1990, a drug-prevention television special was broadcast on ABC, NBC, and CBS named Cartoon All-Stars to the Rescue that featured some of the most popular cartoons at the time; representing TMNT was Michelangelo, voiced by Townsend Coleman.
Starting on September 8, 1990 (with a different opening sequence), the show began its run on CBS. The CBS weekend edition ran for a full hour until 1994, initially airing a few Saturday-exclusive episodes back-to-back. Also, a brief "Turtle Tips" segment aired between the two episodes, which served as public-service announcement about the environment or other issues. After 1994, the show was reduced to just a half-hour and only eight episodes per season were produced, grouped into a "CBS Action Zone" block that also featured WildC.A.T.s. and Skeleton Warriors, both of which were canceled after one season; though TMNTs retained their "Action Zone" introduction. The two shows in the block were also produced by Fred Wolf Films. The series ran until November 2, 1996, when it aired its final episode. Its enormous popularity gave rise to its numerous imitators, including the Battletoads, Cheetahmen, Wild West C.O.W.-Boys of Moo Mesa, Road Rovers, Street Sharks, Extreme Dinosaurs, and Biker Mice from Mars. Currently, all 193 episodes are available on DVD and VHS.
Original video animation[edit]
Main article: Mutant Turtles: Choujin Densetsu-hen
In addition to the American series, a Japan-exclusive two-episode anime original video animation (OVA) series was made in 1996, titled Mutant Turtles: Choujin Densetsu-hen. The OVA is similar in tone to the 1987 TV series and uses the same voices from TV Tokyo's Japanese dub of the 1987 TV series. The first episode was made to advertise the TMNT Supermutants toys. It featured the Turtles as superheroes, that gained costumes and superpowers with the use of Mutastones, while Shredder, Bebop and Rocksteady gained supervillain powers with the use of a Dark Mutastone. As with the Super Sentai and Power Rangers franchises, the four Turtles could combine to form the giant Turtle Saint. The second episode was created to advertise the Metal Mutants toys in which the characters gain Saint Seiya-esque mystical metal armor that can transform into beasts.
Live-action series (1997–1998)[edit]
Logo of the live-action series
Main article: Ninja Turtles: The Next Mutation
In 1997–1998, the Turtles starred in a live-action television series called Ninja Turtles: The Next Mutation that directly follows the events of the first three movies. A fifth turtle was introduced, a female named Venus de Milo, who was skilled in the mystical arts of the shinobi.[15] The series was intended as a loose continuation of the movie franchise, as Shredder had been defeated and the Ninja Turtles encountered new villains. Other connections to the feature films include the fact that Splinter's ear was cut, the Foot Soldiers were humans, and the Turtles lived in the abandoned subway station seen in the second and third movies. The Next Mutation Turtles made a guest appearance on Power Rangers in Space.[18] It was canceled after one season of 26 episodes.
Second animated series (2003–2009)[edit]
Logo of the 2003 cartoon
Main article: Teenage Mutant Ninja Turtles (2003 TV series)
In 2003, a new TMNT series produced by 4Kids Entertainment began airing on the "FoxBox" (later renamed "4Kids TV") programming block. It later moved to "The CW4Kids" block. The series was co-produced by Mirage Studios,[19] and Mirage owned one-third of the rights to the series. Mirage's significant stake in creative control resulted in a cartoon that hews more closely to the original comics, creating a darker and edgier feel than the 1987 cartoon, but still remains lighthearted enough to be considered appropriate for children.
This series lasted until 2009, ending with a feature-length television movie titled Turtles Forever, which was produced in conjunction with the 25th anniversary of the TMNTs franchise and featured the Turtles of the 2003 series teaming up with their counterparts from the 1987 series. 4Kidstv.com featured all the episodes of the series, until September 2010, when Nickelodeon brought the series and air the series occasionally on Nicktoons and Nickelodeon normally during TMNTs marathons.
Third animated series (2012–2017)[edit]
Logo of the 2012 cartoon
Main article: Teenage Mutant Ninja Turtles (2012 TV series)
Nickelodeon acquired the global rights to Teenage Mutant Ninja Turtles from the Mirage Group and 4Kids Entertainment, Inc. and announced a new CGI-animated TMNT television series.[20][21][22] The series is currently in its fifth and final season. The 2012 version is characterized by anime-like iconography and emphasis on mutagen continuing to wreak havoc on the everyday lives of the Turtles and their enemies.
Fourth animated series (2018)[edit]
Nickelodeon announced a new 2D animated series based on the franchise titled Rise of the Teenage Mutant Ninja Turtles, which will debut in Fall 2018.[23][24]
Feature films[edit]
Main article: Teenage Mutant Ninja Turtles (film series)
The Turtles have appeared in six feature films. The first three are live-action features produced in the early 1990s: Teenage Mutant Ninja Turtles (1990), Teenage Mutant Ninja Turtles II: The Secret of the Ooze (1991), and Teenage Mutant Ninja Turtles III (1993). The Turtles were played by various actors in costumes featuring animatronic heads, initially produced by Jim Henson's Creature Shop. The fourth film is a CGI-animated film titled simply TMNT and released in 2007.
A reboot, titled Teenage Mutant Ninja Turtles produced by Platinum Dunes, Nickelodeon Movies, and Paramount Pictures, directed by Jonathan Liebesman, and produced by Michael Bay, was released on August 8, 2014.[8] A sequel, Out of the Shadows was released on June 3, 2016.[25]
Merchandise[edit]
Among the first licensed products to feature the TMNT was a tabletop role-playing game titled Teenage Mutant Ninja Turtles & Other Strangeness, published by Palladium Books in 1985, and featuring original comics and illustrations by Eastman and Laird. The game features a large list of animals, including elephants and sparrows, that are available as mutant player characters. Several more titles were in this genre, including Teenage Mutant Ninja Turtles Adventures, Truckin' Turtles, Turtles Go Hollywood, Teenage Mutant Ninja Turtles Guide to the Universe, and Transdimensional Teenage Mutant Ninja Turtles.
In 1986, Dark Horse Miniatures in Boise, Idaho, produced an attendant set of lead figurines; unlike later incarnations, the bandannas on the store's display set were painted all black before the multicolored versions were released to help younger readers distinguish between the four characters other than their weaponry. Palladium allowed the license to lapse in 2000, in part due to declining sales stemming from the "kiddification" of the animated and live-action incarnations to that point. However, Palladium's publisher, Kevin Siembieda, has indicated a potential willingness to revisit the license given the franchise's recent moves closer to its roots.[26]
Toys[edit]
Main article: Teenage Mutant Ninja Turtles action figures
During the run of the 1987 TV series, Playmates Toys produced hundreds of TMNT action figures, along with vehicles, playsets, and accessories, becoming one of the top collectibles for children.[27] Staff artists at Northampton, Massachusetts-based Mirage Studios provided conceptual designs for many of the figures, vehicles, and playsets and creator credit can be found in the legal text printed on the back of the toy packaging. In addition, Playmates produced a series of TMNTs/Star Trek crossover figures, due to Playmates holding the Star Trek action-figure license at the time. Playmates employed many design groups to develop looks and styles for the toy line, including Bloom Design, White Design, Pangea, Robinson-Clarke, and McHale Design. The marketing vice president of Playmates, Karl Aaronian, was largely responsible for assembling the talented team of designers and writers, which in turn, helped germinate continued interest in the toy line.
Never before in toy history did an action-figure line have such an impact for over two decades, generating billions of dollars in licensing revenue. The series was highly popular in the UK, where in the run-up to Christmas, the Army & Navy Store in London's Lewisham devoted its entire basement to everything Turtle, including games, videos, costumes, and other items. Playmates continue to produce TMNT action figures based on the 2003 animated series. The 2007 film TMNT also gave Playmates a new source from which to make figures, while National Entertainment Collectibles Association produced a series of high-quality action figures based on character designs from the original Mirage comics. In 2012, a new toy line and a new classic toy line from Playmates were announced to be released.[28]
Video games[edit]
Main article: List of Teenage Mutant Ninja Turtles video games
The first console video game based on the franchise, titled Teenage Mutant Ninja Turtles, was released for the Nintendo Entertainment System (NES) by Konami under their "Ultra Games" label in 1989 and later ported to home computers and eventually for the Wii on the Virtual Console. Also released by Konami in 1989 was an arcade game, also titled simply Teenage Mutant Ninja Turtles, later ported to the NES as Teenage Mutant Ninja Turtles II: The Arcade Game, leading to an NES-only sequel, Teenage Mutant Ninja Turtles III: The Manhattan Project, which used the look of the arcade game, as opposed to the first NES game. The next Turtles game, Teenage Mutant Ninja Turtles: Turtles in Time, was released in 1991 as an arcade game, and was later ported to the Super Nintendo Entertainment System (Super NES) in 1992. Teenage Mutant Ninja Turtles: The Hyperstone Heist was also created for the Sega Genesis in the same year, and used many of the art assets from TMNT IV. There was also a trilogy of TMNT video games for the original Game Boy system made by Konami, consisting of: Teenage Mutant Ninja Turtles: Fall of the Foot Clan, Teenage Mutant Ninja Turtles II: Back from the Sewers, and Teenage Mutant Ninja Turtles III: Radical Rescue. As the video game series progressed, and the Ninja Turtles' popularity began to decline in the mid-1990s, the video games changed direction. Teenage Mutant Ninja Turtles: Tournament Fighters was released as a set of one-on-one fighting game similar to the Street Fighter series; versions were released for the NES, SNES, and Genesis, each a distinct game.
Konami also acquired the license to adapt the 2003 TV series into a video game franchise, resulting in a new series of games with 3D gameplay inspired by the old TMNT beat 'em up games, consisting of Teenage Mutant Ninja Turtles (2003 video game), Teenage Mutant Ninja Turtles 2: Battle Nexus, and Teenage Mutant Ninja Turtles 3: Mutant Nightmare.
In 2006, Ubisoft acquired the rights for TMNT games, beginning with a game based on the 2007 animated feature film, along with a distinct game for the Game Boy Advance similar in style to the Konami arcade games.[29][30] A beat 'em up game Teenage Mutant Ninja Turtles: Arcade Attack was released for the Nintendo DS in 2009, to coincide with the series' 25th anniversary.[31] In 2013, Activision released the downloadable game Teenage Mutant Ninja Turtles: Out of the Shadows, based on the 2012 TV series and developed by Red Fly Studio for the Xbox Live Arcade, PlayStation Network and Steam.[32]
On January 25, 2016, Activision and PlatinumGames announced Teenage Mutant Ninja Turtles: Mutants in Manhattan for the PlayStation 4, PlayStation 3, Xbox One, Xbox 360, and PC. The game is described as a third-person, team-based brawler. The campaign will be playable either single-player or co-op and will have an original story written by Tom Waltz, IDW comic writer and editor. The art style is based on long time TMNT comic artist Mateus Santolouco.[33]
Teenage Mutant Ninja Turtles Legends, a Free to play Role-playing video game has been released by Ludia in summer 2016 for iPhone, iPad, Android, and Kindle Fire. It is based on the Teenage Mutant Ninja Turtles (2012 TV series).
In other media[edit]
Tabletop role playing game[edit]
In 1985 Palladium published Teenage Mutant Ninja Turtles & Other StrangenessISBN 0-916211-14-2. This was a stand-alone game, as well as acting as an expansion for their Rifts Megaverse. Within the game players rolled percentile dice or chose an animal, its physical attributes, the cause for mutation and education. The process involved spending Bio-Energy (Bio-E) to customise the animal to indicate how it had changed. The cost varied by animal depending on how developed the trait already was. e.g. Apes could pay 5 Bio-E for fully human hands, whereas Birds would have to pay 20.
The game used many key mechanics from the Palladium system. Character alignment is broadly covered by 3 groups, Good, Selfish and Evil. Education splits into Groups of Scholastic Skills and those Secondary skills the character has picked up in life. The combat system, including Hit Points (HP) and Structural Damage Capacity (SDC) are in there. The game itself is limited to which Martial Arts are available, but a separate book, Ninjas and Superspies ISBN 0-916211-31-2 increased the amount available from the generic Hand to Hand: Basic / Expert / Martial Arts or Ninjitsu to a choice of 41 Martial Arts styles.
Examples of animals created are included in the Appendices as potential Antagonists ; the Terror Bears; Caesers Weasels; Sparrow Eagles, as well as including stats for the Turtles and other characters.
Food tie-ins[edit]
Main article: Teenage Mutant Ninja Turtles food tie-ins
During the height of their popularity, the Turtles had a number of food tie-ins.[34] Among the most notable of these products was Ninja Turtles Cereal, produced by Ralston-Purina as a kind of "Chex with TMNT-themed marshmallows" which also came with a small pouch of Pizza Crunchabungas, pizza-flavored corn snacks in the shape of pizzas (the commercial starred the Ninja Turtles as Will Vinton-created claymations); Hostess Ninja Turtles Pudding Pies, featuring a green sugar crust and vanilla pudding inside; and Royal OOZE Gelatin Desserts, distributed by Nabisco under "Royal Gelatin" in three different flavors: orange, strawberry, and lime. Shreddies used to give out TMNT toys in their boxes when the cereal advertising was still geared toward children. One example of a TMNT prize was rings featuring a character on the cartoon (1992). There was also green Ninja Turtle ice cream with different toppings according to which turtle flavor one ordered. Chef Boyardee also released a canned pasta with the pasta in the shapes of the four turtles.[35]
Concert tour[edit]
To capitalize on the Turtles' popularity, a concert tour was held in 1990, premiering at Radio City Music Hall on August 17.[36][37] The "Coming Out of Their Shells" tour featured live-action turtles playing music as a band (Donatello, keyboards; Leonardo, bass guitar; Raphael, drums and sax; Michelangelo, guitar) on stage around a familiar plotline: April O'Neil is kidnapped by the Shredder, and the turtles have to rescue her.[38] The story had a very Bill-n'-Ted-esque feel, with its theme of the power of rock n' roll literally defeating the enemy, in the form of the Shredder (who only rapped about how he hates music) trying to eliminate all music. A pay-per-view special highlighting the concert was shown, and a studio album was also released.[39] The track listing is as follows:
Concert tour track list [show]
"Coming Out of Our Shells!"
"Sing About It"
"Tubin'"
"Skipping Stones"
"Pizza Power"
"Walk Straight"
"No Treaties"
"Cowabunga"
"April Ballad"
"Count on Us"
Since the tour was sponsored by Pizza Hut in real life, many references are made to their pizza. Empty Pizza Hut boxes are seen onscreen in the "Behind the Shells" VHS. As part of a cross-marketing strategy, Pizza Hut restaurants gave away posters, audio cassettes of "Coming Out of Their Shells", and "Official Tour Guides" as premiums. The original show of the tour was released on video with a making of video also released. The song "Pizza Power" was later used by Konami for the second arcade game Teenage Mutant Ninja Turtles: Turtles in Time.
At the Disney-MGM Studios theme park[edit]
On June 30, 1990, the TMNT appeared in the "New York Street" section of Disney-MGM Studios theme park in Orlando. Emerging from their Turtle Party Wagon, they would "ninja dance" across the stage while April performed the theme song to the show. After the main show was done, they posed for pictures and signed autographs. The Turtles also made appearances in Disney's Very Merry Christmas Parade to sing their own rendition of "Santa Claus is Coming to Town". They also appeared during the Easter parade dancing to their single "Pizza Power!" The Turtles' live shows and appearances ceased production in 1996.
Parodies[edit]
Cover of Cracked #255, August 1990
Although the TMNT had originated as something of a parody, the comic's explosive success led to a wave of small-press, black and white comic parodies of TMNT itself, including Adolescent Radioactive Black Belt Hamsters, Pre-Teen Dirty-Gene Kung Fu Kangaroos, and a host of others. Dark Horse Comics' Boris the Bear was launched in response to these TMNT clones; its first issue was titled "Boris the Bear Slaughters the Teenage Radioactive Black Belt Mutant Ninja Critters". Once the Turtles broke into the mainstream, parodies also proliferated in other media, such as in satire magazines Cracked and Mad magazine and numerous TV series of the period. The satirical British television series Spitting Image featured a recurring sketch "Teenage Mutant Ninja Turds".[40]
Controversies[edit]
Departure from origins[edit]
The Turtles engaged in a greater amount of overt violence in the pages of the early Mirage comic book series by Eastman and Laird. As the TMNT were introduced into the mainstream, they were radically redesigned. In issue #19 of Teenage Mutant Ninja Turtles, the creators published an editorial addressing any possible concerns of readers as a result of this. It stated, in part: "We've allowed the wacky side to happen, and enjoy it very much. All the while, though, we've kept the originals very much ours – forty pages of what we enjoy and want to see in our books, whether it comes from our own hands or from those of the talented people we work with."[41] In the film Turtles Forever, the original Mirage Turtles refer to their descendants as "sell-outs", in reference to their colorful accessories (the originals are conveyed in black and white).
Teenage Mutant "Hero" Turtles [edit]
The title screen from the TMHT version, altered due to censorship.
Upon TMNT's first arrival in the United Kingdom and Ireland the name was changed to "Teenage Mutant Hero Turtles" (or TMHT, for short), since local censorship policies deemed the word ninja to have excessively violent connotations for a children's program (in Ireland, however, the first season aired as "Teenage Mutant Ninja Turtles" before the change to "Teenage Mutant Hero Turtles").[42] Consequently, everything related to the Turtles (comic books, video games, toys, etc.) had to be renamed before being released in these nations, as well as in the German-speaking countries.
The lyrics were also changed, such as changing "Splinter taught them to be ninja teens" to "Splinter taught them to be fighting teens". The policies also had other effects, such as editing out use of Michelangelo's nunchaku (which were at the time banned from appearing in 18-rated films and generally toning down the usage of all the turtles' weapons.[43] To head this problem off, the showrunners elected to remove Michelangelo's nunchaku entirely during season three, replacing them with a grappling hook called the "Turtle Line" that served as Mikey's signature weapon for the rest of the show's run.[3]
In Italy, Spain and Portugal, they kept Michelangelo's nunchaku but the "TMHT" logo could be seen in the intro, as it was not edited to reflect the title in each of those translations. In Spain the cartoon was originally aired in regional TV channels and thus had different dubs in addition to Castillian: Galician and Catalan;[citation needed] in the Galician version, the title As Tartarugas Mutantes ("The Mutant Turtles") was used. The Italian and European Portuguese dubs also had few edits.
However, when the live-action movie came out in 1990, the Ninja of the title was kept even in the UK. In time, nunchaku scenes were retained in previously-censored movies such as those of Bruce Lee. The same went for the PAL releases of the early video games, which had Michelangelo's weapon of choice fully visible and usable. By the time of the 2003 TV series, these censorship policies had been abolished, and no changes have occurred in the content of the show. The name "Teenage Mutant Ninja Turtles" remained unchanged for the 2003 TV series. As a result, in the UK, the 1987 TV series is still called Teenage Mutant Hero Turtles and the 2003 TV series is called Teenage Mutant Ninja Turtles. In 2009, Lionsgate Home Entertainment released the 25th Anniversary Collectors Edition on Region 2 DVD in the UK. This 3-Disc set contains all the episodes of Seasons 1 and 2 and 4 episodes from the final season, as well as a 1-Disc DVD with the first few episodes of Season 1. This release features the original, unedited episodes under the "Ninja Turtles" title, and also marks the first time the show has been released and left uncensored in the UK.[citation needed]
Ownership rights[edit]
Due to various movie and television deals, the various TMNT films and television series have split between various companies, with Mirage Studios having retained copyright and trademark until October 19, 2009, at which point the rights for the entire TMNT franchise were sold by co-creator Peter Laird to Nickelodeon.[44]
Television[edit]
The original animated series (1987–1996) was produced by Fred Wolf Films Dublin (as Murakami Wolf Swenson (MWS) and Murakami Wolf Dublin (MWD) during earlier seasons), and syndicated by Group W. The series itself is owned by Wolf Films, with home entertainment rights residing with Lions Gate Entertainment, and until recently, syndication rights belonged to Nickelodeon's former corporate sibling CBS Television Distribution.[citation needed] The initial five-part miniseries (retroactively considered the first season) was copyrighted by Playmates Toys, although their rights to those episodes were bought out by Fred Wolf Films.
Ninja Turtles: The Next Mutation was produced by Saban Entertainment, and as of September 2011, is owned and distributed by Saban Brands.[45][46][47]
The second animated series (2003–2009) was a co-production between Mirage Studios and 4Kids Entertainment. Nickelodeon's October 19, 2009 buyout of the TMNT franchise included an approximate $9.75 million payment to 4Kids to terminate its right to serve as the merchandise licensing agent prior to the scheduled expiration of the representation agreement in 2012.[7][48] Due to the buyout, all future TMNT film and television series rights are owned by Nickelodeon.[44] Nickelodeon also gained the rights to the 2003 series after terminating 4Kids' contract.
Films[edit]
The first three TMNT live-action films were produced by Golden Harvest, with New Line Cinema (now a sister company of Warner Bros. Entertainment) distributing the films in the United States, with 20th Century Fox distributing the second and third films in most other territories. The first two films were copyrighted by the UK-based Northshore Investments. The third film was copyrighted by Clearwater Holdings. The fourth film was produced by Imagi Animation Studios, and released by Warner Bros. Entertainment in association with the Weinstein Company.
Michael Bay produced a feature film directed by Jonathan Liebesman simply titled Teenage Mutant Ninja Turtles, and was released on August 8, 2014. A sequel, Teenage Mutant Ninja Turtles: Out of the Shadows, was released on June 3, 2016, with Megan Fox and Will Arnett reprising their roles and debuting Stephen Amell as Casey Jones. Dave Green replaced Liebesman as the director.
Comic books[edit]
Initially, Mirage allowed employees and freelancers to retain the rights to characters they created for the TMNT Universe but had never licensed for media and merchandise outside comic books. Eventually, due to the difficulty of keeping track of everyone's rights, Mirage made TMNT character creators sign retroactive work-for-hire contracts. One creator who did not sign over the rights to his TMNT work was Swamp Thing veteran Rick Veitch.[49]
See also[edit]
Comics portal
1980s portal
Table of Teenage Mutant Ninja Turtles character appearances
List of anthropomorphic animal superheroes
Ninja in popular culture
References[edit]
Jump up ^ "Heroes in a Half Shell Turn the Big 2–5". The New York Times. April 20, 2009. Retrieved November 9, 2010.
Jump up ^ Greenberg, Harvey R. (April 15, 1990). "Just How Powerful Are Those Turtles?". The New York Times. Retrieved August 7, 2010.
^ Jump up to: a b "TMNT: The Rennaissance [sic&] Reptiles Return". Kung Fu Magazine. Retrieved December 27, 2009.
Jump up ^ "I Was a Teenage Mutant Ninja Turtle". January 26, 2007. Archived from the original on January 3, 2010.
^ Jump up to: a b Wiater, Stanley (1991). The Official Teenage Mutant Ninja Turtles Treasury. Villard Books. ISBN 0679734848.
Jump up ^ Laird, Peter (October 21, 2009). "palblog: Musings about the sale". Archived from the original on October 26, 2009. Retrieved October 24, 2009.
^ Jump up to: a b "The Mirage Group Sells Teenage Mutant Ninja Turtles to Nickelodeon". Reuters. October 21, 2009. Archived from the original on February 1, 2011. Retrieved August 28, 2016.
^ Jump up to: a b "Teenage Mutant Ninja Turtles (2014)". IMDb. Retrieved July 22, 2014.
^ Jump up to: a b TMNT Origin Story, official site. Retrieved November 16, 2007. Archived June 1, 2012, at the Wayback Machine.
Jump up ^ McGill, Douglas C. (December 25, 1988). "DYNAMIC DUO: Kevin Eastman and Peter Laird; Turning Teenage Mutant Ninja Turtles Into a Monster". The New York Times. Retrieved August 7, 2010.
Jump up ^ "History of the Ninja Turtles". TeenageMutantNinjaTurtles.com. TeenageMutantNinjaTurtles.com. Retrieved June 2, 2016.
Jump up ^ IDW Announces New Comic Series Based on the Original Teenage Mutant Ninja Turtles Archived April 7, 2011, at the Wayback Machine. IDW Publishing April 1, 2011 Accessed April 7, 2011
Jump up ^ About the Creators TMNT25.com (January 2009). Retrieved on 1–31–09. Archived April 20, 2009, at the Wayback Machine.
Jump up ^ Simpson, Janice C. (April 2, 1990). "Show Business: Lean, Green and on the Screen". Time. Retrieved March 3, 2010.
^ Jump up to: a b "Teenage Mutant Ninja Turtles On TV". IGN. Retrieved August 15, 2010.
Jump up ^ "Teenage Mutant Ninja Turtles" (1987/I) – Trivia IMDB.com (February 2019). Retrieved on 2–21–09.
Jump up ^ "The Official TMNT Web Site!". Tmnt25.com. Archived from the original on April 14, 2009. Retrieved August 10, 2013.
Jump up ^ "Teenage Mutant Ninja Turtles On TV". IGN. Retrieved August 15, 2010.
Jump up ^ "TMNT Celebrates 25 Years, III – Peter Laird". Newsarama. Retrieved August 22, 2010.
Jump up ^ Cruz, Eileen (April 4, 2011). "WonderCon 2011 – PR: IDW to Publish New Ninja Turtles Series Based on Original Comics". toonzone news. Archived from the original on December 8, 2012. Retrieved April 5, 2011.
Jump up ^ David McCutcheon (March 9, 2011). "TMNT Gets a Makeover". IGN TV. Retrieved April 5, 2011.
Jump up ^ Eric Goldman (October 21, 2009). "New Ninja Turtles TV Series and Film Coming". IGN TV. Retrieved April 5, 2011.
Jump up ^ Steinberg, Brian (March 2, 2017). "Nickelodeon Rouses SpongeBob, Green Slime, ‘Lip Sync Battle’ and Gwen Stefani to Lure Upfront Dollars".
Jump up ^ "Nickelodeon unveils 2017 upfront lineup". kidscreen.com.
Jump up ^ Bahr, Lindsay (August 10, 2014). "'Teenage Mutant Ninja Turtles' sequel set for 2016". Entertainment Weekly. Retrieved September 14, 2015.
Jump up ^ Meadows, Chris (February 19, 2007). "Kevin Siembieda Interview, Part 2" (mp3). Space Station Liberty. Retrieved February 20, 2007.
Jump up ^ Lazzareschi, Carla (December 23, 1991). "Rapid-Paced Turtle Sales Starting to Slow Down : Toys: Rival manufacturers see a cooling of the 'Ninja' fad as a chance to regain a larger share of the market.". The Los Angeles Times. Retrieved November 9, 2010.
Jump up ^ "Playmates Reveals 2012 'Teenage Mutant Ninja Turtles' Action Figures – ComicsAlliance | Comic book culture, news, humor, commentary, and reviews". ComicsAlliance. Archived from the original on June 18, 2013. Retrieved April 29, 2013.
Jump up ^ "Ubisoft to create video game based on 2007 TMNT movie". Starpulse.com. January 11, 2006. Retrieved August 10, 2013.
Jump up ^ "4Kids Entertainment And The Mirage Group Sign Worldwide Video Game Agreement With Ubisoft" (PDF). 4kidsentertainment.com. January 11, 2006. Archived from the original (PDF) on June 14, 2006. Retrieved August 28, 2016.
Jump up ^ Teenage Mutant Ninja Turtles: Arcade Attack hands-on ign.com
Jump up ^ "Mutant Ninja Turtles: Out of the Shadows announced – trailer". Digitalspy.co.uk. March 4, 2013. Retrieved August 10, 2013.
Jump up ^ "TMNT - Mutants in Manhattan". www.tmntmutantsinmanhattan.com. Retrieved January 26, 2016.
Jump up ^ Hunt, Dennis (April 13, 1990). "'Turtles' Tapes Being Served at Burger King". The Los Angeles Times. Retrieved November 9, 2010.
Jump up ^ "Mutant Merchandise". Entertainment Weekly. March 30, 1990. Retrieved December 7, 2010.
Jump up ^ Givens, Ron (August 17, 1990). "Music news for August 17, 1990 – Prince and the Teenage Mutant Ninja Turtles made news this week". Entertainment Weekly. Retrieved December 7, 2010.
Jump up ^ Pareles, Jon (September 28, 1990). "Review/Music; After the Hype, an Elaborate High-Tech Show for the Ninja Turtles Set". The New York Times. Retrieved November 9, 2010.
Jump up ^ Granberry, Ted; Churnin, Nancy (November 30, 1990). "Turtles Shell Out Ninja Concert Fun". The Los Angeles Times. Retrieved August 27, 2010.
Jump up ^ "Shell Schlocked". Entertainment Weekly. October 12, 1990. Retrieved December 7, 2010.
Jump up ^ https://www.youtube.com/watch?v=rX924HL3pV0&feature=youtu.be&t=18m59s
Jump up ^ Teenage Mutant Ninja Turtles vol. 1 #19, March 1989.
Jump up ^ Cohen, Susan (April 7, 1991). "Teenage Mutant Ninja Television: Who's winning the battle over kids' TV?". Washington Post Magazine.
Jump up ^ "FAQ". Ninjaturtles.com. Archived from the original on May 4, 2012. Retrieved August 10, 2013.
^ Jump up to: a b Hall, Peter. "So Much for a Dark and Twisted 'Teenage Mutant Ninja Turtles' Movie". amazon.imdb.com. Retrieved October 22, 2009.
Jump up ^ "Programming Catalog: Ninja Turtles: The Next Mutation". MarVista Entertainment. Archived from the original on March 25, 2012. Retrieved September 16, 2011.
Jump up ^ "Cynopsis: Kids! 09/19/11". Cynopsis. September 19, 2011. Archived from the original on July 24, 2012. Retrieved September 19, 2011.
Jump up ^ Pickard, Michael (September 16, 2011). "MarVista picks up live Turtles". C21Media. Archived from the original on October 12, 2011. Retrieved September 19, 2011.
Jump up ^ "The Mirage Group Sells Teenage Mutant Ninja Turtles to Nickelodeon-4Kids Entertainment to End Long-Standing Relationship as Teenage Mutant Ninja Turtles Licensing Agent and Production Partner" (PDF). 4kidsentertainment.com. October 21, 2009. Archived from the original (PDF) on December 29, 2009. Retrieved August 28, 2016.
Jump up ^ "The Kevin Eastman Interview Part I|The Comics Journal". Tcj.com. January 3, 2012. Retrieved August 10, 2013.
Bibliography[edit]
Eastman, Kevin (2002). Kevin Eastman's Teenage Mutant Ninja Turtles Artobiography. Los Angeles: Heavy Metal. ISBN 1-882931-85-8.
Wiater, Stanley (1991). The Official Teenage Mutant Ninja Turtles Treasury. New York: Villard. ISBN 0-679-73484-8.
External links[edit]
Wikimedia Commons has media related to Teenage Mutant Ninja Turtles.
Wikiquote has quotations related to: Teenage Mutant Ninja Turtles
Official website
Teenage Mutant Ninja Turtles at Don Markstein's Toonopedia
[hide]
v
t
e
Teenage Mutant Ninja Turtles
Created by
Kevin Eastman
Peter Laird
Characters
(appearances)
Turtles
Leonardo
Donatello
Michelangelo
Raphael
Supporting
Splinter
Hamato Yoshi
April O'Neil
Casey Jones
Leatherhead
Metalhead
Miyamoto Usagi
Mighty Mutanimals
Venus
Antagonists
Shredder
Foot Clan
Karai
Baxter Stockman
Bebop and Rocksteady
Krang
Purple Dragons
Rat King
Slash
Tokka and Rahzar
Comics
Mirage comic series
Tales
Adventures
Mighty Mutanimals
Daily comic strip
Dreamwave comics series
IDW comic series
Television
1987 series
Episodes
Season 1
Season 2
Season 3
Season 4
Season 5
Season 6
Season 7
Season 8
Season 9
Season 10
Mutant Turtles: Superman Legend
Next Mutation
Episodes
Villains
2003 series
Episodes
Season 1
Season 2
Season 3
Season 4
Season 5
Season 6
Season 7
Turtles Forever
Home video
2012 series
Characters
Episodes
Season 1
Season 2
Season 3
Season 4
Season 5
Films
Teenage Mutant Ninja Turtles (1990)
soundtrack
II: The Secret of the Ooze (1991)
soundtrack
III (1993)
soundtrack
TMNT (2007)
soundtrack
Teenage Mutant Ninja Turtles (2014)
soundtrack
Out of the Shadows (2016)
Games
Role-playing games
Video games
Other
Action figures
Lego
Alien races
Casey Jones (fan film)
Food tie-ins
Cartoon All-Stars to the Rescue
"Turtle Power!"
"Spin That Wheel"
Dimension X
Technodrome
Teenage Mutant Ninja Turtles Shell Shock
Turtle Power: The Definitive History of the Teenage Mutant Ninja Turtles
Category
Retrieved from "https://en.wikipedia.org/w/index.php?title=Teenage_Mutant_Ninja_Turtles&oldid=803764097"
Categories:
Superhero teams
Teenage Mutant Ninja Turtles
1984 comics debuts
Animal superheroes
Anthropomorphic martial artists
Child superheroes
American comics adapted into films
Comics adapted into animated films
Comics adapted into television series
Comics adapted into plays
Comics adapted into animated series
Comics adapted into video games
Comics characters introduced in 1984
Corporate mascots
Fictional mutants
Fictional ninja
Fictional turtles
Fictional comedians
Image Comics teams
Mirage Studios titles
Viacom Media Networks
Nickelodeon
Ninja parody
Robots in television
Teens in fiction
Hidden categories:
Webarchive template wayback links
Use American English from February 2015
All Wikipedia articles written in American English
Use mdy dates from May 2016
Articles needing additional references from May 2016
All articles needing additional references
Groups pop
Articles needing additional references from April 2015
Wikipedia articles needing clarification from June 2015
Articles containing Japanese-language text
All articles with unsourced statements
Articles with unsourced statements from April 2013
Articles with unsourced statements from October 2009
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
Azərbaycanca
Български
Català
Čeština
Dansk
Deutsch
Ελληνικά
Español
Esperanto
فارسی
Føroyskt
Français
한국어
Հայերեն
हिन्दी
Hrvatski
Bahasa Indonesia
Interlingua
Íslenska
Italiano
עברית
ქართული
Kernowek
Latina
Latviešu
Magyar
Bahasa Melayu
Nederlands
日本語
Norsk
Norsk nynorsk
Oʻzbekcha/ўзбекча
Piemontèis
Polski
Português
Română
Русский
Scots
Simple English
Slovenčina
Slovenščina
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
ไทย
Тоҷикӣ
Türkçe
Українська
اردو
Tiếng Việt
ייִדיש
中文
Edit links
This page was last edited on 4 October 2017, at 13:45.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

attrs: href class title

values: Teenage Mutant Ninja Turtles (disambiguation)

attrs: role class

values:
note
hatnote navigation-not-searchable

values: Help:Introduction to referencing with Wiki Markup/1

values: plainlinks metadata ambox ambox-content ambox-Refimprove

attrs: alt src width height data-file-width data-file-height

values: Teenage Mutant Ninja Turtles (Kevin Eastman's art).jpg

values: Teenage Mutant Ninja Turtles (Mirage Studios)

values: Donatello (Teenage Mutant Ninja Turtles)

values: Michelangelo (Teenage Mutant Ninja Turtles)

values: width:22em;width: 24em; background: #f2f9ff;

values:
/wiki/Alien_invader
mw-redirect
Alien invader

values:
/wiki/High_concept
mw-redirect
High concept

values: The text near this tag may need clarification or removal of jargon. (June 2015)

values:
noprint Inline-Template
margin-left:0.1em; white-space:nowrap;

values: Teenage Mutant Ninja Turtles (1987 TV series)

values: Teenage Mutant Ninja Turtles action figures

values:
/wiki/Pez_dispenser
mw-redirect
Pez dispenser

values: Teenage Mutant Ninja Turtles (1990 film)

values: Teenage Mutant Ninja Turtles (film series)

values: Teenage Mutant Ninja Turtles (2003 TV series)

values: Teenage Mutant Ninja Turtles (2014 film)

values: List of Teenage Mutant Ninja Turtles characters

values: Teenage Mutant Ninja Turtles (2012 TV series)

values: Teenage Mutant Ninja Turtles (IDW Publishing)

values:
/wiki/TMNT_(2007_film)
mw-redirect
TMNT (2007 film)

values: Casey Jones (Teenage Mutant Ninja Turtles)

values:
/wiki/Hockey_mask
mw-redirect
Hockey mask

values: Tales of the Teenage Mutant Ninja Turtles

values:
/wiki/Jim_Lawson_(comic_book_writer)
mw-redirect
Jim Lawson (comic book writer)

values: Edit section: Teenage Mutant Ninja Turtles Adventures

values: Teenage Mutant Ninja Turtles (Dreamwave Productions)

values: Teenage Mutant Ninja Turtles (comic strip)

values: Edit section: First animated series (1987–1996)

values:
/wiki/Fred_Wolf_Films_Dublin
mw-redirect
Fred Wolf Films Dublin

values:
/wiki/Splinter_(TMNT)
mw-redirect
Splinter (TMNT)

values:
/wiki/Shredder_(TMNT)
mw-redirect
Shredder (TMNT)

values:
/wiki/Dimension_X_(TMNT)
mw-redirect
Dimension X (TMNT)

values:
/wiki/African_American
mw-redirect
African American

values: Edit section: Live-action series (1997–1998)

values: Edit section: Second animated series (2003–2009)

values:
/wiki/4Kids_Entertainment
mw-redirect
4Kids Entertainment

values:
/wiki/The_CW4Kids
mw-redirect
The CW4Kids

values: Edit section: Third animated series (2012–2017)

values: Edit section: Fourth animated series (2018)

values: Teenage Mutant Ninja Turtles II: The Secret of the Ooze

values: Teenage Mutant Ninja Turtles: Out of the Shadows

values: Teenage Mutant Ninja Turtles & Other Strangeness

values: Teenage Mutant Ninja Turtles Adventures (role-playing game supplement)

values: Teenage Mutant Ninja Turtles Guide to the Universe

values: Transdimensional Teenage Mutant Ninja Turtles

values: National Entertainment Collectibles Association

values: List of Teenage Mutant Ninja Turtles video games

values: Teenage Mutant Ninja Turtles (arcade game)

values: Teenage Mutant Ninja Turtles III: The Manhattan Project

values: Teenage Mutant Ninja Turtles: Turtles in Time

values: Teenage Mutant Ninja Turtles: The Hyperstone Heist

values: Teenage Mutant Ninja Turtles: Fall of the Foot Clan

values: Teenage Mutant Ninja Turtles II: Back from the Sewers

values: Teenage Mutant Ninja Turtles III: Radical Rescue

values: Teenage Mutant Ninja Turtles: Tournament Fighters

values: Teenage Mutant Ninja Turtles (2003 video game)

values: Teenage Mutant Ninja Turtles 2: Battle Nexus

values: Teenage Mutant Ninja Turtles 3: Mutant Nightmare

values: Teenage Mutant Ninja Turtles: Out of the Shadows (video game)

values: Teenage Mutant Ninja Turtles: Mutants in Manhattan

values: Edit section: Tabletop role playing game

values:
/wiki/Ninjas_and_Superspies
mw-redirect
Ninjas and Superspies

values: Teenage Mutant Ninja Turtles food tie-ins

values:
/wiki/Hostess_(brand)
mw-redirect
Hostess (brand)

values:
/wiki/Rock_n%27_roll
mw-redirect
Rock n' roll

values: text-align: left; display: none; background: transparent;

values:
NavFrame collapsed
border:#aaa 1px solid;
NavFrame1

values: Edit section: At the Disney-MGM Studios theme park

values: Adolescent Radioactive Black Belt Hamsters

values: Edit section: Teenage Mutant "Hero" Turtles

attrs: alt src width height class data-file-width data-file-height

values: 18 (British Board of Film Classification)

values: This claim needs references to reliable sources. (April 2013)

values:
noprint Inline-Template Template-Fact
white-space:nowrap;

values:
/wiki/Lions_Gate_Entertainment
mw-redirect
Lions Gate Entertainment

values: This claim needs references to reliable sources. (October 2009)

values:
/wiki/Warner_Bros._Entertainment
mw-redirect
Warner Bros. Entertainment

values:
/wiki/TMNT_(movie)
mw-redirect
TMNT (movie)

values: display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle

values: margin:0.5em 0 0.5em 1em;border:solid #aaa 1px

values: List of anthropomorphic animal superheroes

values:
nofollow
http://www.imdb.com/title/tt1291150/
external text

values:
/wiki/Internet_Movie_Database
mw-redirect
Internet Movie Database

values:
nofollow
http://www.tmntmutantsinmanhattan.com/
external text

values:
nofollow
http://amazon.imdb.com/news/ni1106749/
external text

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

values: commons:Category:Teenage Mutant Ninja Turtles

values:
nofollow
http://www.ninjaturtles.com/
external text

values:
nofollow
external text
http://www.toonopedia.com/turtles.htm

values: Template talk:Teenage Mutant Ninja Turtles

values:
navbox-abovebelow
2
background: #CDF89F;

values: Leatherhead (Teenage Mutant Ninja Turtles)

values: Metalhead (Teenage Mutant Ninja Turtles)

values: List of Teenage Mutant Ninja Turtles (1987 TV series) episodes

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 1)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 2)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 3)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 4)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 5)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 6)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 7)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 8)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 9)

values: Teenage Mutant Ninja Turtles (1987 TV series) (season 10)

values: List of Ninja Turtles: The Next Mutation episodes

values: List of Ninja Turtles: The Next Mutation villains

values: List of Teenage Mutant Ninja Turtles (2003 TV series) episodes

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 1)

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 2)

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 3)

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 4)

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 5)

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 6)

values: Teenage Mutant Ninja Turtles (2003 TV series) (season 7)

values: List of Teenage Mutant Ninja Turtles (2003) home video releases

values: List of Teenage Mutant Ninja Turtles (2012 TV series) characters

values: List of Teenage Mutant Ninja Turtles (2012 TV series) episodes

values: Teenage Mutant Ninja Turtles (2012 TV series) (season 1)

values: Teenage Mutant Ninja Turtles (2012 TV series) (season 2)

values: Teenage Mutant Ninja Turtles (2012 TV series) (season 3)

values: Teenage Mutant Ninja Turtles (2012 TV series) (season 4)

values: Teenage Mutant Ninja Turtles (2012 TV series) (season 5)

values: Teenage Mutant Ninja Turtles: The Original Motion Picture Soundtrack

values: Teenage Mutant Ninja Turtles II: The Secret of the Ooze: The Original Motion Picture Soundtrack

values: Teenage Mutant Ninja Turtles III: Original Motion Picture Soundtrack

values: Teenage Mutant Ninja Turtles: Music from the Motion Picture

values: List of Teenage Mutant Ninja Turtles alien races

values: Dimension X (Teenage Mutant Ninja Turtles)

values: Teenage Mutant Ninja Turtles Shell Shock

values: nowraplinks hlist collapsible autocollapse navbox-inner

values: Category:American comics adapted into films

values: Category:Comics adapted into animated films

values: Category:Comics adapted into television series

values: Category:Comics adapted into animated series

values: Category:Comics adapted into video games

values: Category:Comics characters introduced in 1984

values: Category:Webarchive template wayback links

values: Category:Use American English from February 2015

values: Category:All Wikipedia articles written in American English

values: Category:Articles needing additional references from May 2016

values: Category:All articles needing additional references

values: Category:Articles needing additional references from April 2015

values: Category:Wikipedia articles needing clarification from June 2015

values: Category:Articles containing Japanese-language text

values: Category:All articles with unsourced statements

values: Category:Articles with unsourced statements from April 2013

values: Category:Articles with unsourced statements from October 2009

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Teenage_Mutant_Ninja_Turtles
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: Костенурките нинджа – Bulgarian

values: Χελωνονιντζάκια – Greek

values: لاک‌پشت‌های نینجا – Persian

values: 닌자 거북이 – Korean

values: Նինջա - կրիաներ – Armenian

values: टीनेज म्यूटेंट निंजा टर्टल्स – Hindi

values: Teenage Mutant Ninja Turtles – Interlingua

values: צבי הנינג'ה – Hebrew

values: კუ ნინძები – Georgian

values: Tini Nindzsa Teknőcök (képregény) – Hungarian

values: ティーンエイジ・ミュータント・ニンジャ・タートルズ – Japanese

values: Teenage Mutant Ninja Turtles – Norwegian

values: Teenage Mutant Ninja Turtles – Norwegian Nynorsk

values: Teenage Mutant Ninja Turtles – Piedmontese

values: Черепашки-ниндзя – Russian

values: Teenage Mutant Ninja Turtles – Simple English

values: Mladé ninja korytnačky (všeobecne) – Slovak

values: Нинџа корњаче – Serbian

values: Teini-ikäiset mutanttininjakilpikonnat – Finnish

values: เต่านินจา – Thai

values: Cанг‌пуштҳои Нинҷа Навҷавон Чаҳишёфта – Tajik

values: Черепашки Ніндзя – Ukrainian

values: ٹین ایج میوٹینٹ ننجا ٹرٹلز – Urdu

values: Teenage Mutant Ninja Turtles – Vietnamese

values: נינדזשא טשערעפאכעס – Yiddish

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Teenage_Mutant_Ninja_Turtles rootpage-Teenage_Mutant_Ninja_Turtles vector-nav-directionality skin-vector action-view


text:
Linear equation
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. (January 2016)
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2016) (Learn how and when to remove this template message)
Graph sample of linear equations.
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable (however, different variables may occur in different terms). A simple example of a linear equation with only one variable, x, may be written in the form: ax + b = 0, where a and b are constants and a ≠ 0. The constants may be numbers, parameters, or even non-linear functions of parameters, and the distinction between variables and parameters may depend on the problem (for an example, see linear regression).
Linear equations can have one or more variables. An example of a linear equation with three variables, x, y, and z, is given by: ax + by + cz + d = 0, where a, b, c, and d are constants and a, b, and c are non-zero. Linear equations occur frequently in most subareas of mathematics and especially in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state. An equation is linear if the sum of the exponents of the variables of each term is one.
Equations with exponents greater than one are non-linear. An example of a non-linear equation of two variables is axy + b = 0, where a and b are constants and a ≠ 0. It has two variables, x and y, and is non-linear because the sum of the exponents of the variables in the first term, axy, is two.
This article considers the case of a single equation for which one searches the real solutions. All its content applies for complex solutions and, more generally for linear equations with coefficients and solutions in any field.
Contents
[hide]
1 One variable
2 Two variables
2.1 Forms for two-dimensional linear equations
2.1.1 General (or standard) form
2.1.2 Slope–intercept form
2.1.3 Point–slope form
2.1.4 Two-point form
2.1.5 Intercept form
2.1.6 Matrix form
2.1.7 Parametric form
2.1.8 2D vector determinant form
2.1.9 Special cases
2.2 Connection with linear functions
2.3 Examples
3 More than two variables
4 See also
5 Notes
6 References
7 External links
One variable[edit]
A linear equation in one unknown x may always be rewritten
a x = b . {\displaystyle ax=b.}
If a ≠ 0, there is a unique solution
x = b a . {\displaystyle x={\frac {b}{a}}.}
If a = 0, then, when b = 0 every number is a solution of the equation, but if b ≠ 0 there are no solutions (and the equation is said to be inconsistent.)
Two variables[edit]
A common form of a linear equation in the two variables x and y is
y = m x + b , {\displaystyle y=mx+b,\,}
where m and b designate constants (parameters). The origin of the name "linear" comes from the fact that the set of solutions of such an equation forms a straight line in the plane. In this particular equation, the constant m determines the slope or gradient of that line, and the constant term b determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.
Since terms of linear equations cannot contain products of distinct or equal variables, nor any power (other than 1) or other function of a variable, equations involving terms such as xy, x2, y1/3, and sin(x) are nonlinear.
Forms for two-dimensional linear equations[edit]
Linear equations can be rewritten using the laws of elementary algebra into several different forms. These equations are often referred to as the "equations of the straight line." In what follows, x, y, t, and θ are variables; other letters represent constants (fixed numbers).
General (or standard) form[edit]
In the general (or standard[1]) form the linear equation is written as:
A x + B y = C , {\displaystyle Ax+By=C,\,}
where A and B are not both equal to zero. The equation is usually written so that A ≥ 0, by convention. The graph of the equation is a straight line, and every straight line can be represented by an equation in the above form. If A is nonzero, then the x-intercept, that is, the x-coordinate of the point where the graph crosses the x-axis (where, y is zero), is C/A. If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis (where x is zero), is C/B, and the slope of the line is −A/B. The general form is sometimes written as:
a x + b y + c = 0 , {\displaystyle ax+by+c=0,\,}
where a and b are not both equal to zero. The two versions can be converted from one to the other by moving the constant term to the other side of the equal sign.
Slope–intercept form[edit]
y = m x + b , {\displaystyle y=mx+b,}
where m is the slope of the line and b is the y intercept, which is the y coordinate of the location where the line crosses the y axis. This can be seen by letting x = 0, which immediately gives y = b. It may be helpful to think about this in terms of y = b + mx; where the line passes through the point (0, b) and extends to the left and right at a slope of m. Vertical lines, having undefined slope, cannot be represented by this form.
Point–slope form[edit]
y − y 1 = m ( x − x 1 ) , {\displaystyle y-y_{1}=m(x-x_{1}),\,}
where m is the slope of the line and (x1,y1) is any point on the line.
The point-slope form expresses the fact that the difference in the y coordinate between two points on a line (that is, y − y1) is proportional to the difference in the x coordinate (that is, x − x1). The proportionality constant is m (the slope of the line).
Two-point form[edit]
y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) , {\displaystyle y-y_{1}={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}(x-x_{1}),\,}
where (x1, y1) and (x2, y2) are two points on the line with x2 ≠ x1. This is equivalent to the point-slope form above, where the slope is explicitly given as (y2 − y1)/(x2 − x1).
Multiplying both sides of this equation by (x2 − x1) yields a form of the line generally referred to as the symmetric form:
( x 2 − x 1 ) ( y − y 1 ) = ( y 2 − y 1 ) ( x − x 1 ) . {\displaystyle (x_{2}-x_{1})(y-y_{1})=(y_{2}-y_{1})(x-x_{1}).\,}
Expanding the products and regrouping the terms leads to the general form:
x ( y 2 − y 1 ) − y ( x 2 − x 1 ) = x 1 y 2 − x 2 y 1 {\displaystyle x\,(y_{2}-y_{1})-y\,(x_{2}-x_{1})=x_{1}y_{2}-x_{2}y_{1}}
Using a determinant, one gets a determinant form, easy to remember:
| x y 1 x 1 y 1 1 x 2 y 2 1 | = 0 . {\displaystyle {\begin{vmatrix}x&y&1\\x_{1}&y_{1}&1\\x_{2}&y_{2}&1\end{vmatrix}}=0\,.}
Intercept form[edit]
x a + y b = 1 , {\displaystyle {\frac {x}{a}}+{\frac {y}{b}}=1,\,}
where a and b must be nonzero. The graph of the equation has x-intercept a and y-intercept b. The intercept form is in standard form with A/C = 1/a and B/C = 1/b. Lines that pass through the origin or which are horizontal or vertical violate the nonzero condition on a or b and cannot be represented in this form.
Matrix form[edit]
Using the order of the standard form
A x + B y = C , {\displaystyle Ax+By=C,\,}
one can rewrite the equation in matrix form:
( A B ) ( x y ) = ( C ) . {\displaystyle {\begin{pmatrix}A&B\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}={\begin{pmatrix}C\end{pmatrix}}.}
Further, this representation extends to systems of linear equations.
A 1 x + B 1 y = C 1 , {\displaystyle A_{1}x+B_{1}y=C_{1},\,}
A 2 x + B 2 y = C 2 , {\displaystyle A_{2}x+B_{2}y=C_{2},\,}
becomes:
( A 1 B 1 A 2 B 2 ) ( x y ) = ( C 1 C 2 ) . {\displaystyle {\begin{pmatrix}A_{1}&B_{1}\\A_{2}&B_{2}\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}={\begin{pmatrix}C_{1}\\C_{2}\end{pmatrix}}.}
Since this extends easily to higher dimensions, it is a common representation in linear algebra, and in computer programming. There are named methods for solving system of linear equations, like Gauss-Jordan which can be expressed as matrix elementary row operations.
Parametric form[edit]
x = T t + U {\displaystyle x=Tt+U\,}
and
y = V t + W . {\displaystyle y=Vt+W.\,}
Two simultaneous equations in terms of a variable parameter t, with slope m = V / T, x-intercept (VU - WT) / V and y-intercept (WT - VU) / T. This can also be related to the two-point form, where T = p - h, U = h, V = q - k, and W = k:
x = ( p − h ) t + h {\displaystyle x=(p-h)t+h\,}
and
y = ( q − k ) t + k . {\displaystyle y=(q-k)t+k.\,}
In this case t varies from 0 at point (h,k) to 1 at point (p,q), with values of t between 0 and 1 providing interpolation and other values of t providing extrapolation.
2D vector determinant form[edit]
The equation of a line can also be written as the determinant of two vectors. If P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} are unique points on the line, then P {\displaystyle P} will also be a point on the line if the following is true:
det ( P 1 P → , P 1 P 2 → ) = 0. {\displaystyle \det({\overrightarrow {P_{1}P}},{\overrightarrow {P_{1}P_{2}}})=0.}
One way to understand this formula is to use the fact that the determinant of two vectors on the plane will give the area of the parallelogram they form. Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.
To expand on this we can say that P 1 = ( x 1 , y 1 ) {\displaystyle P_{1}=(x_{1},\,y_{1})} , P 2 = ( x 2 , y 2 ) {\displaystyle P_{2}=(x_{2},\,y_{2})} and P = ( x , y ) {\displaystyle P=(x,\,y)} . Thus P 1 P → = ( x − x 1 , y − y 1 ) {\displaystyle {\overrightarrow {P_{1}P}}=(x-x_{1},\,y-y_{1})} and P 1 P 2 → = ( x 2 − x 1 , y 2 − y 1 ) {\displaystyle {\overrightarrow {P_{1}P_{2}}}=(x_{2}-x_{1},\,y_{2}-y_{1})} , then the above equation becomes:
det ( x − x 1 y − y 1 x 2 − x 1 y 2 − y 1 ) = 0. {\displaystyle \det {\begin{pmatrix}x-x_{1}&y-y_{1}\\x_{2}-x_{1}&y_{2}-y_{1}\end{pmatrix}}=0.}
Thus,
( x − x 1 ) ( y 2 − y 1 ) − ( y − y 1 ) ( x 2 − x 1 ) = 0. {\displaystyle (x-x_{1})(y_{2}-y_{1})-(y-y_{1})(x_{2}-x_{1})=0.}
Ergo,
( x − x 1 ) ( y 2 − y 1 ) = ( y − y 1 ) ( x 2 − x 1 ) . {\displaystyle (x-x_{1})(y_{2}-y_{1})=(y-y_{1})(x_{2}-x_{1}).}
Then dividing both side by ( x 2 − x 1 ) {\displaystyle (x_{2}-x_{1})} would result in the “Two-point form” shown above, but leaving it here allows the equation to still be valid when x 1 = x 2 {\displaystyle x_{1}=x_{2}} .
Special cases[edit]
y = b {\displaystyle y=b\,}
Horizontal Line y = b
This is a special case of the standard form where A = 0 and B = 1, or of the slope-intercept form where the slope m = 0. The graph is a horizontal line with y-intercept equal to b. There is no x-intercept, unless b = 0, in which case the graph of the line is the x-axis, and so every real number is an x-intercept.
x = a {\displaystyle x=a\,}
Vertical Line x = a
This is a special case of the standard form where A = 1 and B = 0. The graph is a vertical line with x-intercept equal to a. The slope is undefined. There is no y-intercept, unless a = 0, in which case the graph of the line is the y-axis, and so every real number is a y-intercept. This is the only type of straight line which is not the graph of a function (it obviously fails the vertical line test).
Connection with linear functions[edit]
A linear equation, written in the form y = f(x) whose graph crosses the origin (x,y) = (0,0), that is, whose y-intercept is 0, has the following properties:
f ( x 1 + x 2 ) = f ( x 1 ) + f ( x 2 ) {\displaystyle f(x_{1}+x_{2})=f(x_{1})+f(x_{2})\ }
and
f ( a x ) = a f ( x ) , {\displaystyle f(ax)=af(x),\,}
where a is any scalar. A function which satisfies these properties is called a linear function (or linear operator, or more generally a linear map). However, linear equations that have non-zero y-intercepts, when written in this manner, produce functions which will have neither property above and hence are not linear functions in this sense. They are known as affine functions.
Examples[edit]
An everyday example of the use of different forms of linear equations is computation of tax with tax brackets. This is commonly done with a progressive tax computation, using either point–slope form or slope–intercept form.
More than two variables[edit]
A linear equation can involve more than two variables. Every linear equation in n unknowns may be rewritten
a 1 x 1 + a 2 x 2 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=b,}
where, a1, a2, ..., an represent numbers, called the coefficients, x1, x2, ..., xn are the unknowns, and b is called the constant term. When dealing with three or fewer variables, it is common to use x, y and z instead of x1, x2 and x3.
If all the coefficients are zero, then either b ≠ 0 and the equation does not have any solution, or b = 0 and every set of values for the unknowns is a solution.
If at least one coefficient is nonzero, a permutation of the subscripts allows to suppose a1 ≠ 0, and rewrite the equation
x 1 = b a 1 − a 2 a 1 x 2 − ⋯ − a n a 1 x n . {\displaystyle x_{1}={\frac {b}{a_{1}}}-{\frac {a_{2}}{a_{1}}}x_{2}-\cdots -{\frac {a_{n}}{a_{1}}}x_{n}.}
In other words, if ai ≠ 0, one may choose arbitrary values for all the unknowns except xi, and express xi in term of these values.
If n = 3 the set of the solutions is a plane in a three-dimensional space. More generally, the set of the solutions is an (n – 1)-dimensional hyperplane in a n-dimensional Euclidean space (or affine space if the coefficients are complex numbers or belong to any field).
See also[edit]
Line (geometry)
System of linear equations
Linear equation over a ring
Algebraic equation
Linear belief function
Linear inequality
Notes[edit]
Jump up ^ Barnett, Ziegler & Byleen 2008, pg. 15
References[edit]
Barnett, R.A.; Ziegler, M.R.; Byleen, K.E. (2008), College Mathematics for Business, Economics, Life Sciences and the Social Sciences (11th ed.), Upper Saddle River, N.J.: Pearson, ISBN 0-13-157225-3
External links[edit]
Linear Equations and Inequalities Open Elementary Algebra textbook chapter on linear equations and inequalities.
Hazewinkel, Michiel, ed. (2001) [1994], "Linear equation", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
[hide]
v
t
e
Polynomials and polynomial functions
By degree
Zero polynomial (degree undefined or −1 or −∞)
Constant function (0)
Linear function (1)
Quadratic function (2)
Cubic function (3)
Quartic function (4)
Quintic function (5)
Sextic equation (6)
Septic equation (7)
Octic equation (8)
By number of terms and other properties
Monomial
Binomial
Trinomial
Homogeneous
Quasi-homogeneous
Tools and algorithms
Factorization
Greatest common divisor
Division
Horner's method of evaluation
Resultant
Discriminant
Gröbner basis
Retrieved from "https://en.wikipedia.org/w/index.php?title=Linear_equation&oldid=809348990"
Categories:
Polynomials
Elementary algebra
Equations
Hidden categories:
Articles needing additional references from January 2016
All articles needing additional references
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
Afrikaans
አማርኛ
العربية
Беларуская
Беларуская (тарашкевіца)
Български
Català
Čeština
Dansk
Deutsch
Eesti
Ελληνικά
Español
Esperanto
Euskara
فارسی
Français
Galego
한국어
Հայերեն
हिन्दी
Hrvatski
Bahasa Indonesia
Íslenska
Italiano
עברית
Қазақша
Latina
Latviešu
Lietuvių
Lumbaart
Magyar
Македонски
മലയാളം
Монгол
Nederlands
日本語
Napulitano
Norsk nynorsk
Oʻzbekcha/ўзбекча
ភាសាខ្មែរ
Polski
Português
Română
Русский
සිංහල
Simple English
Slovenčina
Slovenščina
کوردی
Srpskohrvatski / српскохрватски
Suomi
Svenska
தமிழ்
ไทย
Türkçe
Українська
اردو
Tiếng Việt
West-Vlams
中文
Edit links
This page was last edited on 8 November 2017, at 15:35.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

key: html

type: local

value: div

attrs: id class

values: mw-page-base noprint

values: mw-head-base noprint

value: a

attrs: id class lang

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

value: img

attrs: alt src width height srcset data-file-width data-file-height

attrs: href class

value: td

attrs: href title

value: b

attrs: class href

value: span

value: i

value: small

value: tr

value: tbody

value: table

attrs: class role

values: plainlinks metadata ambox ambox-content ambox-one_source

values: Help:Introduction to referencing with Wiki Markup/1

values: plainlinks metadata ambox ambox-content ambox-Refimprove

attrs: alt src width height class srcset data-file-width data-file-height

values:
/wiki/Term_(mathematics)
mw-redirect
Term (mathematics)

values:
/wiki/Non-linear_equation
mw-redirect
Non-linear equation

values: vertical-align: -0.338ex; width:7.355ex; height:2.176ex;

values: vertical-align: -1.838ex; width:7.183ex; height:5.343ex;

values:
/wiki/Inconsistent_equations
mw-redirect
Inconsistent equations

values: vertical-align: -0.671ex; width:12.569ex; height:2.509ex;

values:
/wiki/Straight_line
mw-redirect
Straight line

values: Edit section: Forms for two-dimensional linear equations

values: Edit section: General (or standard) form

values: vertical-align: -0.671ex; width:14.815ex; height:2.676ex;

values: vertical-align: -0.671ex; width:16.8ex; height:2.509ex;

values: vertical-align: -0.671ex; width:12.182ex; height:2.509ex;

values: vertical-align: -0.838ex; width:20.855ex; height:2.843ex;

values: vertical-align: -2.171ex; width:27.295ex; height:5.176ex;

values: vertical-align: -0.838ex; width:39.223ex; height:2.843ex;

values: vertical-align: -0.838ex; width:39.905ex; height:2.843ex;

values: vertical-align: -4.171ex; width:17.823ex; height:9.509ex;

values: vertical-align: -2.005ex; width:12.355ex; height:5.009ex;

values: vertical-align: -2.505ex; width:22.091ex; height:6.176ex;

values: vertical-align: -0.671ex; width:17.895ex; height:2.676ex;

values: vertical-align: -2.505ex; width:28.395ex; height:6.176ex;

values: vertical-align: -0.505ex; width:11.977ex; height:2.343ex;

values: vertical-align: -0.671ex; width:13.264ex; height:2.509ex;

values: vertical-align: -0.838ex; width:17.097ex; height:2.843ex;

values: vertical-align: -0.838ex; width:17.225ex; height:2.843ex;

values: Edit section: 2D vector determinant form

values: vertical-align: -0.671ex; width:2.564ex; height:2.509ex;

values: vertical-align: -0.338ex; width:1.756ex; height:2.176ex;

values: vertical-align: -0.838ex; width:20.872ex; height:4.176ex;

values: vertical-align: -0.838ex; width:13.548ex; height:2.843ex;

values: vertical-align: -0.838ex; width:10.633ex; height:2.843ex;

values: vertical-align: -0.838ex; width:23.768ex; height:4.176ex;

values: vertical-align: -0.838ex; width:26.519ex; height:4.176ex;

values: vertical-align: -2.505ex; width:30.031ex; height:6.176ex;

values: vertical-align: -0.838ex; width:42.859ex; height:2.843ex;

values: vertical-align: -0.838ex; width:38.836ex; height:2.843ex;

values: vertical-align: -0.838ex; width:9.485ex; height:2.843ex;

values: vertical-align: -0.671ex; width:7.912ex; height:2.009ex;

values: vertical-align: -0.671ex; width:5.67ex; height:2.509ex;

values: vertical-align: -0.338ex; width:6.076ex; height:1.676ex;

values: Edit section: Connection with linear functions

values: vertical-align: -0.838ex; width:28.356ex; height:2.843ex;

values: vertical-align: -0.838ex; width:15.553ex; height:2.843ex;

values:
/wiki/Affine_function
mw-redirect
Affine function

values: vertical-align: -0.671ex; width:30.5ex; height:2.509ex;

values: vertical-align: -2.171ex; width:32ex; height:5.676ex;

values:
reflist mw-references-wrap
list-style-type: decimal;

values:
/wiki/Polynomial_function
mw-redirect
Polynomial function

values:
/wiki/Zero_polynomial
mw-redirect
Zero polynomial

values: nowraplinks collapsible autocollapse navbox-inner

values: Category:Articles needing additional references from January 2016

values: Category:All articles needing additional references

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Linear_equation
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values:
uls-settings-trigger
Language settings
0
button
true

values: ሊኒያር እኩልዮሽ – Amharic

values: معادلة خطية – Arabic

values: Лінейнае ўраўненне – Belarusian

values: Лінейнае раўнаньне – Belarusian (Taraškievica orthography)

values: Линейно уравнение – Bulgarian

values: Εξίσωση ευθείας – Greek

values: معادله خطی – Persian

values: 일차 방정식 – Korean

values: Գծային հավասարում – Armenian

values: रेखीय समीकरण – Hindi

values: משוואה לינארית – Hebrew

values: Сызықтық теңдеу – Kazakh

values: Линеарна равенка – Macedonian

values: രേഖീയസമവാക്യം – Malayalam

values: Шугаман тэгшитгэл – Mongolian

values: សមីការដឺក្រេទី១ – Khmer

values: Линейное уравнение – Russian

values: ඒකජ සමීකරණ – Sinhala

values: நேரியல் சமன்பாடு – Tamil

values: สมการเชิงเส้น – Thai

values: Лінійне рівняння – Ukrainian

values: لکیری مساوات – Urdu

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Linear_equation rootpage-Linear_equation vector-nav-directionality skin-vector action-view