{"id":5612,"date":"2016-03-01t10:30:46","date_gmt":"2016-03-01t18:30:46","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=5612"},"modified":"2016-03-01t10:26:32","modified_gmt":"2016-03-01t18:26:32","slug":"act-math-tips-the-one-equation-of-a-line-you-need-to-know","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/act\/act-math-tips-the-one-equation-of-a-line-you-need-to-know\/","title":{"rendered":"act math tips: the one equation of a line you need to know"},"content":{"rendered":"<p><a href=\"https:\/\/www.youtube.com\/watch?v=qm_dittat-8&#038;feature=youtu.be\">https:\/\/www.youtube.com\/watch?v=qm_dittat-8&amp;feature=youtu.be<\/a><\/p>\n<p>in geometry class, there are several forms of an equation of a line that most students learn.<\/p>\n<p>you learn standard form, slope-intercept form, point-slope form, etc., but for basically every single question that the act math section asks you about lines on a coordinate plane, there\u2019s only one you really need to know. only one that is really useful.<\/p>\n<p>the winner is&#8230;slope-intercept form, or <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_5f96ed7246eea7b15460adc977781742.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"y = mx + b\" title=\"y = mx + b\"\/>.<\/p>\n<p>ding! ding! ding!<\/p>\n<p>slope-intercept form is so useful because, in order to answer many questions on the act, you will need to find: either the slope or the y-intercept, or you will be given the slope and a point and need to find the y-intercept, or something along those lines.<\/p>\n<p>if you put an equation in slope-intercept form,<img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_5f96ed7246eea7b15460adc977781742.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"y = mx + b\" title=\"y = mx + b\"\/>, you will see this information instantaneously. in the equation <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_5f96ed7246eea7b15460adc977781742.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"y = mx + b\" title=\"y = mx + b\"\/>:<\/p>\n<ul>\n<li><em>m<\/em> is the slope.<\/li>\n<li>b is the y-intercept<\/li>\n<\/ul>\n<p>so if an equation of a line is in this form, you don\u2019t need to do any extra work to determine what these values are.<\/p>\n<p>the act knows how powerful slope-intercept form is, so it will rarely give you an equation in this form. instead, it will typically give lines in standard form, ax + by = c. so what you want to do, in most cases, is use your algebra skills to move this equation around to slope-intercept form.<\/p>\n<p>let\u2019s say you have this equation of a line: <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_240b3a02b4516061827e5f536ff9de5c.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"2x + 4y = 12\" title=\"2x + 4y = 12\"\/>. move it around so that you have the y isolated on one side:<\/p>\n<ul>\n<li><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_240b3a02b4516061827e5f536ff9de5c.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"2x + 4y = 12\" title=\"2x + 4y = 12\"\/><\/li>\n<li><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_6beaa21cc8ed2de54c246dd827463529.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"4y = - 2x + 12\" title=\"4y = - 2x + 12\"\/><\/li>\n<li><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_27978b25f45b8d051720486fea2af400.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"y = (- 2x + 12)\/4\" title=\"y = (- 2x + 12)\/4\"\/><\/li>\n<li><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_15dc900044c93236b7f96cc65a7ad7e7.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"y = -2\/4 x + 12\/4\" title=\"y = -2\/4 x + 12\/4\"\/><\/li>\n<li><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_43b839eecb32df44cb250497870f31c6.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"y = -1\/2 x + 3\" title=\"y = -1\/2 x + 3\"\/><\/li>\n<\/ul>\n<p>now we can see that the slope of this line is <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_c4b9b6b2c2e12439b84e08a6563bc43a.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"-1\/2\" title=\"-1\/2\"\/>and the y-intercept is 3, and that\u2019s very valuable information.<\/p>\n<p>check out the video above for examples on how this works in real act-like problems!<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>in geometry class, there are several forms of an equation of a line that most students learn.<br \/>\nyou learn standard form, slope-intercept form, point-slope form, etc., but for basically every single question that the act math section asks you about lines on a coordinate plane, there\u2019s only one you really need to know. only one that is really useful.<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[9,7,18],"ppma_author":[24868],"acf":[],"yoast_head":"<!-- this site is optimized with the yoast seo premium plugin v21.7 (yoast seo v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>act math: the one equation of a line you need to know<\/title>\n<meta name=\"description\" content=\"in geometry class, there are several forms of an equation of a line that most students learn, but there\u2019s only one you really need to know for the act.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/act\/act-math-tips-the-one-equation-of-a-line-you-need-to-know\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta 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fracchia","image":{"@type":"imageobject","inlanguage":"en-us","@id":"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/image\/60578a68f08364eae9072dc9e31af74c","url":"https:\/\/secure.gravatar.com\/avatar\/f9dd7c84140858c94c792aa9aae2d486?s=96&d=mm&r=g","contenturl":"https:\/\/secure.gravatar.com\/avatar\/f9dd7c84140858c94c792aa9aae2d486?s=96&d=mm&r=g","caption":"kristin fracchia"},"description":"dr. kristin fracchia has over fifteen years of expertise in college and graduate school admissions and with a variety of standardized tests, including the act, sat, gre, gmat, and lsat, with several 99% scores. she had a phd from the university of california, irvine, an ma degree from the catholic university, and ba degrees in secondary education and english literature from the university of maryland, college park. she was the recipient of the 2013 excellence in teaching award and the chancellor\u2019s club fellowship from the university of california, irvine. she\u2019s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. she now develops accessible and effective edtech products for magoosh. her free online content and youtube videos providing test prep and college admissions advice have received over 6 million views in over 125 countries. kristin is an advocate for improving access to education: you can check out her tedx talk on the topic. follow kristin on linkedin!","sameas":["https:\/\/www.ted.com\/tedx\/events\/27777","https:\/\/www.linkedin.com\/in\/kristinfracchia\/","https:\/\/twitter.com\/kristinfracchia","https:\/\/www.youtube.com\/watch?v=-junkojw4y4"],"honorificprefix":"dr.","honorificsuffix":"phd","award":["2013 excellence in teaching award","chancellor's club fellowship (uci)"],"knowsabout":["act","sat","gre","gmat","lsat"],"jobtitle":"general manager, test prep","worksfor":"magoosh","url":"\/\/www.catharsisit.com\/hs\/author\/kristinkeating\/"}]}},"authors":[{"term_id":24868,"user_id":88,"is_guest":0,"slug":"kristinkeating","display_name":"kristin fracchia","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/f9dd7c84140858c94c792aa9aae2d486?s=96&d=mm&r=g","user_url":"","last_name":"fracchia","first_name":"kristin","description":"dr. kristin fracchia has over fifteen years of expertise in college and graduate school admissions and with a variety of standardized tests, including the act, sat, gre, gmat, and lsat, with several 99% scores. she had a phd from the <a href=\"https:\/\/drama.arts.uci.edu\/graduate-programs\/phd\/alums\">university of california, irvine<\/a>, an ma degree from the catholic university, and ba degrees in secondary education and english literature from the university of maryland, college park. she was the recipient of the 2013 excellence in teaching award and the <a href=\"https:\/\/grad.uci.edu\/funding\/fellowships-awards\/internal\/chancellors-club-fellows.php\">chancellor\u2019s club fellowship<\/a> from the university of california, irvine. she\u2019s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. she now develops accessible and effective edtech products for magoosh. her free online content and<a href=\"https:\/\/www.youtube.com\/watch?v=-junkojw4y4\"> youtube videos<\/a> providing test prep and college admissions advice have received over 6 million views in over 125 countries. kristin is an advocate for improving access to education: you can check out her<a href=\"https:\/\/www.ted.com\/tedx\/events\/27777\"> tedx<\/a> talk on the<a href=\"https:\/\/www.youtube.com\/watch?v=pf41qj80vwy\"> topic<\/a>. follow kristin on<a href=\"https:\/\/www.linkedin.com\/in\/kristinfracchia\/\"> linkedin<\/a>!"}],"_links":{"self":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts\/5612"}],"collection":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/users\/88"}],"replies":[{"embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/comments?post=5612"}],"version-history":[{"count":0,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts\/5612\/revisions"}],"wp:attachment":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/media?parent=5612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/categories?post=5612"},{"taxonomy":"post_tag","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/tags?post=5612"},{"taxonomy":"author","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/ppma_author?post=5612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}