{"id":248132,"date":"2025-07-08T07:00:51","date_gmt":"2025-07-08T07:00:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248132"},"modified":"2025-07-08T07:00:53","modified_gmt":"2025-07-08T07:00:53","slug":"rewrite-each-of-the-following-equations-in-y-mx-b-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/rewrite-each-of-the-following-equations-in-y-mx-b-form\/","title":{"rendered":"Rewrite each of the following equations in y = mx + b form."},"content":{"rendered":"\n<p>Rewrite each of the following equations in y = mx + b form. Show each step! 1) x + y = -15 2) 2y + 8x = 1 3) -2x + y = 1 4) 3y &#8211; 2x = 9 5) 2y = -1x &#8211; 8 6) y &#8211; 4 = -3(x &#8211; 3) 2014-2015<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1) x+y=\u221215x + y = -15x+y=\u221215<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by isolating yyy. To do this, subtract xxx from both sides of the equation. x+y\u2212x=\u221215\u2212xx + y &#8211; x = -15 &#8211; xx+y\u2212x=\u221215\u2212x y=\u2212x\u221215y = -x &#8211; 15y=\u2212x\u221215<\/li>\n<\/ul>\n\n\n\n<p>This is now in y=mx+by = mx + by=mx+b form with m=\u22121m = -1m=\u22121 and b=\u221215b = -15b=\u221215.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2) 2y+8x=12y + 8x = 12y+8x=1<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First, subtract 8x8x8x from both sides. 2y=\u22128x+12y = -8x + 12y=\u22128x+1<\/li>\n\n\n\n<li>Now, divide the entire equation by 2 to solve for yyy. 2y2=\u22128&#215;2+12\\frac{2y}{2} = \\frac{-8x}{2} + \\frac{1}{2}22y\u200b=2\u22128x\u200b+21\u200b y=\u22124x+12y = -4x + \\frac{1}{2}y=\u22124x+21\u200b<\/li>\n<\/ul>\n\n\n\n<p>Now it&#8217;s in the form y=mx+by = mx + by=mx+b, where m=\u22124m = -4m=\u22124 and b=12b = \\frac{1}{2}b=21\u200b.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3) \u22122x+y=1-2x + y = 1\u22122x+y=1<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by isolating yyy. Add 2x2x2x to both sides. y=2x+1y = 2x + 1y=2x+1<\/li>\n<\/ul>\n\n\n\n<p>This is in the form y=mx+by = mx + by=mx+b with m=2m = 2m=2 and b=1b = 1b=1.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4) 3y\u22122x=93y &#8211; 2x = 93y\u22122x=9<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Add 2x2x2x to both sides to get the yyy-terms isolated. 3y=2x+93y = 2x + 93y=2x+9<\/li>\n\n\n\n<li>Now, divide by 3 to solve for yyy. y=2&#215;3+3y = \\frac{2x}{3} + 3y=32x\u200b+3<\/li>\n<\/ul>\n\n\n\n<p>In the form y=mx+by = mx + by=mx+b, m=23m = \\frac{2}{3}m=32\u200b and b=3b = 3b=3.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5) 2y=\u2212x\u221282y = -x &#8211; 82y=\u2212x\u22128<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide both sides of the equation by 2 to solve for yyy. y=\u2212x2\u22124y = \\frac{-x}{2} &#8211; 4y=2\u2212x\u200b\u22124<\/li>\n<\/ul>\n\n\n\n<p>So the equation is y=\u221212x\u22124y = -\\frac{1}{2}x &#8211; 4y=\u221221\u200bx\u22124, with m=\u221212m = -\\frac{1}{2}m=\u221221\u200b and b=\u22124b = -4b=\u22124.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">6) y\u22124=\u22123(x\u22123)y &#8211; 4 = -3(x &#8211; 3)y\u22124=\u22123(x\u22123)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First, distribute the \u22123-3\u22123 on the right-hand side. y\u22124=\u22123x+9y &#8211; 4 = -3x + 9y\u22124=\u22123x+9<\/li>\n\n\n\n<li>Now, add 4 to both sides to isolate yyy. y=\u22123x+9+4y = -3x + 9 + 4y=\u22123x+9+4 y=\u22123x+13y = -3x + 13y=\u22123x+13<\/li>\n<\/ul>\n\n\n\n<p>Now it\u2019s in the form y=mx+by = mx + by=mx+b, with m=\u22123m = -3m=\u22123 and b=13b = 13b=13.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Summary:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>y=\u2212x\u221215y = -x &#8211; 15y=\u2212x\u221215<\/li>\n\n\n\n<li>y=\u22124x+12y = -4x + \\frac{1}{2}y=\u22124x+21\u200b<\/li>\n\n\n\n<li>y=2x+1y = 2x + 1y=2x+1<\/li>\n\n\n\n<li>y=2&#215;3+3y = \\frac{2x}{3} + 3y=32x\u200b+3<\/li>\n\n\n\n<li>y=\u221212x\u22124y = -\\frac{1}{2}x &#8211; 4y=\u221221\u200bx\u22124<\/li>\n\n\n\n<li>y=\u22123x+13y = -3x + 13y=\u22123x+13<\/li>\n<\/ol>\n\n\n\n<p>These are all in slope-intercept form, and you can easily identify the slope and y-intercept in each case.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-157.jpeg\" alt=\"\" class=\"wp-image-248133\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Rewrite each of the following equations in y = mx + b form. Show each step! 1) x + y = -15 2) 2y + 8x = 1 3) -2x + y = 1 4) 3y &#8211; 2x = 9 5) 2y = -1x &#8211; 8 6) y &#8211; 4 = -3(x &#8211; 3) 2014-2015 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-248132","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=248132"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248132\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}