{"id":313,"date":"2022-04-13T09:01:35","date_gmt":"2022-04-13T09:01:35","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=313"},"modified":"2025-08-20T01:33:02","modified_gmt":"2025-08-20T01:33:02","slug":"t-8-slope-intercept-form-write-an-equation","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-8-slope-intercept-form-write-an-equation\/","title":{"rendered":"T.8 Slope-intercept form: write an equation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Slope-intercept form: write an equation<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwPL5mQ7s\/bkBJMI2sZQzWIg0O-0T4yQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwPL5mQ7s&#x2F;bkBJMI2sZQzWIg0O-0T4yQ&#x2F;watch?utm_content=DAGwPL5mQ7s&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.8 Slope-intercept form: write an equation<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-a6eadf443dfa9ca6be729c7ba7603663\" style=\"color:#000060\"><strong> What is Slope-Intercept Form?<\/strong><\/h2>\n\n\n\n<p>A line can be written in the <strong>slope-intercept form<\/strong>:<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"><strong><em>y<\/em>&nbsp;= m<em>x<\/em>&nbsp;+ b<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left has-normal-font-size\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m = <strong>slope<\/strong> of the line (steepness)<\/li>\n\n\n\n<li>b = <strong>y-intercept<\/strong> (the point where the line crosses the y-axis)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-ecdcdd08ba02d122b41dfd7d60c8e404\" style=\"color:#000060\"><strong>Formula Recap: Slope<\/strong><\/h2>\n\n\n\n<p>The slope between two points (x<sub>1<\/sub>,y<sub>1<\/sub>)\u200b and (x<sub>2<\/sub>,y<sub>2<\/sub>) is: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>m=y<sub>2<\/sub>\u2212y<sub>1<\/sub>\/x<sub>2<\/sub>\u2212x<sub>1<\/sub><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-dc30123cc00f71ee89e8379df2da849e\" style=\"color:#000060\"><strong> Writing the Equation \u2013 Given Slope and Y-Intercept<\/strong><\/h2>\n\n\n\n<p>If you know mmm and bbb, simply substitute into: <\/p>\n\n\n\n<p class=\"has-text-align-center\">y=mx+b<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Slope m=3, y-intercept b=\u22122 <\/p>\n\n\n\n<p class=\"has-text-align-center\"> y=3x\u22122<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-b669e256c18d240376d47b45a69354cb\" style=\"color:#000060\"><strong>Writing the Equation \u2013 Given Slope and a Point<\/strong><\/h2>\n\n\n\n<p class=\"has-text-align-center\">If you know mmm and a point  (x<sub>1<\/sub>,y<sub>1<\/sub>), use the <strong>point-slope form<\/strong> first: y\u2212y<sub>1<\/sub>=m(x\u2212x<sub>1<\/sub>)<\/p>\n\n\n\n<p>Then, rearrange into y=mx+b.<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Slope m=\u22124point (2, 5)<\/p>\n\n\n\n<p class=\"has-text-align-center\"> y\u22125=\u22124(x\u22122)<\/p>\n\n\n\n<p class=\"has-text-align-center\">y\u22125=\u22124x+8<\/p>\n\n\n\n<p class=\"has-text-align-center\">y=\u22124x+13<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-5bb55f93ade85e0b4217cbabb97ceb00\" style=\"color:#000060\"><strong>Writing the Equation \u2013 Given Two Points<\/strong><\/h2>\n\n\n\n<p>1.Find the slope mmm using: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>m=y<sub>2<\/sub>\u2212y<sub>1<\/sub>\/x<sub>2<\/sub>\u2212x<sub>1<\/sub><\/strong><\/p>\n\n\n\n<p>2.Use one of the points and point-slope form to find b.<\/p>\n\n\n\n<p>3.Write the final equation in slope-intercept form.<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Points (1, 2) and (3, 6)<br>Step 1: <\/p>\n\n\n\n<p class=\"has-text-align-center\">m=6\u22122\/3\u22121=4\/2=2<\/p>\n\n\n\n<p>Step 2: Using (1, 2): <\/p>\n\n\n\n<p class=\"has-text-align-center\">y\u22122=2(x\u22121)<\/p>\n\n\n\n<p class=\"has-text-align-center\">y = 2x + 0<\/p>\n\n\n\n<p>Final: <\/p>\n\n\n\n<p class=\"has-text-align-center\">y=2xy<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-106a2d49aa30b25d08b43e19e01b5aa5\" style=\"color:#000060\"><strong> Special Cases<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Horizontal line:<\/strong> slope <strong>m=0<\/strong> \u2192 equation is<strong> y=b<\/strong><\/li>\n\n\n\n<li><strong>Vertical line:<\/strong> slope is undefined \u2192 cannot be written in <strong>y=mx+b<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-dd00f406c4062ca6b486241a8d99a10d\" style=\"color:#000060\"><strong>Practice Problems<\/strong><\/h2>\n\n\n\n<p>1. Write the equation of a line with slope 5 and y-intercept -3.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p>2.  Write the equation of a line with slope -2 passing through (4, 7).<\/p>\n\n\n\n<p>3.  Find the equation of the line passing through (0, -2) and (5, 3).<\/p>\n\n\n\n<p>4.  A line has slope 34\\frac{3}{4}43\u200b and passes through (2, -1). Write its equation.<\/p>\n\n\n\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-link-color has-large-font-size wp-elements-2bc79ef7590e2ce8a070a0a5e1ff4416\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#cefdeb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-1d0ebb085e774b1c8116dca79388730d\" style=\"color:#b00012\"><strong>A line&#8217;s y-intercept is 16, and its slope is 8. What is its equation in slope-intercept form?<\/strong><\/p>\n\n\n\n<p>Plug the slope m = 8 and the y-intercept b = 16 into the slope-intercept formula.<br>y = mx + b<\/p>\n\n\n\n<p>y = 8x + 16<\/p>\n\n\n\n<p class=\"has-normal-font-size\">y = 8x \u2212 16<\/p>\n\n\n\n<p>The equation of the line in slope-intercept form is y = 8x \u2212 16.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#dfccfc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-1e3b0b92169b4aa9b4b57620f9e848c2\" style=\"color:#b00012\"><strong>A line&#8217;s slope is 1, and its y-intercept is 19. What is its equation in slope-intercept form?<\/strong><\/p>\n\n\n\n<p>Plug the slope m = 1 and the y-intercept b = 19 into the slope-intercept formula.<br>y = mx + b<\/p>\n\n\n\n<p>y = 1x + 19<\/p>\n\n\n\n<p>y = x + 19<\/p>\n\n\n\n<p>The equation of the line in slope-intercept form is y = x + 19.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#fcccdf\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-29c789805d6aa745743951e76d5d22fe\" style=\"color:#b00012\"><strong>There is a line whose y-intercept is 20 and whose slope is 1. What is its equation in slope-intercept form?<\/strong><\/p>\n\n\n\n<p>Plug the slope m = 1 and the y-intercept b = 20 into the slope-intercept formula.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y = 1x + 20<\/p>\n\n\n\n<p class=\"has-normal-font-size\">y = x + 20<\/p>\n\n\n\n<p>y = x \u2212 20<\/p>\n\n\n\n<p>The equation of the line in slope-intercept form is y = x \u2212 20.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/77927\/810\/537\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-124.png\" alt=\"\" class=\"wp-image-8073\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-124.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-124-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-124-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76980\/653\/382\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-133.png\" alt=\"\" class=\"wp-image-8074\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-133.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-133-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-133-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Slope-intercept form: write an equation T.8 Slope-intercept form: write an equation by Delta publications Key Notes: What is Slope-Intercept Form? A line can be written in the slope-intercept form: y&nbsp;= mx&nbsp;+ b where: Formula Recap: Slope The slope between two points (x1,y1)\u200b and (x2,y2) is: m=y2\u2212y1\/x2\u2212x1 Writing the Equation \u2013 Given Slope and Y-Intercept If<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-8-slope-intercept-form-write-an-equation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.8 Slope-intercept form: write an equation&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-313","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/313","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=313"}],"version-history":[{"count":22,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/313\/revisions"}],"predecessor-version":[{"id":17547,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/313\/revisions\/17547"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}