{"id":307,"date":"2022-04-13T09:00:41","date_gmt":"2022-04-13T09:00:41","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=307"},"modified":"2025-08-18T13:39:31","modified_gmt":"2025-08-18T13:39:31","slug":"t-5-slope-intercept-form-find-the-slope-and-y-intercept","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-5-slope-intercept-form-find-the-slope-and-y-intercept\/","title":{"rendered":"T.5 Slope-intercept form: find the slope and y-intercept"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#060074;text-transform:uppercase\"><strong>Slope-intercept form: find the slope and y-intercept<\/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%; 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; border-radius: 8px; will-change: transform;\"> <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\" src=\"https:\/\/www.canva.com\/design\/DAGwOWPY0aE\/BgbHB0qzO02-17x71bHnMQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\"> <\/iframe> <\/div> <a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwOWPY0aE&#x2F;BgbHB0qzO02-17x71bHnMQ&#x2F;watch?utm_content=DAGwOWPY0aE&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\"> T.5 Slope-intercept form: find the slope and y-intercept<\/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<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-492cb45500548d7e47a446f93e257b4c\" style=\"color:#000060\"><strong>Definition<\/strong><\/h3>\n\n\n\n<p>The <strong>slope-intercept form<\/strong> of a linear equation is:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y = mx + b<\/strong><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>m<\/strong> \u2192 <strong>Slope<\/strong> (rate of change)<\/li>\n\n\n\n<li><strong>b<\/strong> \u2192 <strong>Y-intercept<\/strong> (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<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-08895c73725707d8a11a4851d5a20a1c\" style=\"color:#000060\"><strong>Understanding the Slope (m)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>slope<\/strong> tells how steep the line is and the direction it goes.<\/li>\n\n\n\n<li>Formula to find slope between two points (x1,y1) and (x2,y2):<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>m = y2 \u2212 y1 \/ x2 \u2212 x1<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive slope<\/strong> \u2192 line rises from left to right<\/li>\n\n\n\n<li><strong>Negative slope<\/strong> \u2192 line falls from left to right<\/li>\n\n\n\n<li><strong>Zero slope<\/strong> \u2192 horizontal line<\/li>\n\n\n\n<li><strong>Undefined slope<\/strong> \u2192 vertical line (cannot be written in slope-intercept form)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-4b895513d449508e63715453bf3c082c\" style=\"color:#000060\"><strong>Understanding the Y-Intercept (b)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>y-intercept<\/strong> is the point where the line meets the y-axis.<\/li>\n\n\n\n<li>At the y-intercept, x = 0.<\/li>\n\n\n\n<li>To find bbb, substitute x = 0 into the equation.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-24b3b7cc293eb61c7aa244643ff05036\" style=\"color:#000060\"><strong>Steps to Find the Slope and Y-Intercept from an Equation<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\">Case 1: Equation is already in slope-intercept form y = mx + b<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope = m (coefficient of xxx)<\/li>\n\n\n\n<li>Y-intercept = b<\/li>\n<\/ul>\n\n\n\n<p>Example: y = 2x + 3<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope m=2<\/li>\n\n\n\n<li>Y-intercept b=3 \u2192 Point (0, 3)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\">Case 2: Equation is in standard form A<sub>x<\/sub> + B<sub>y<\/sub> = C<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rearrange into y = mx + b by isolating y.<\/li>\n<\/ul>\n\n\n\n<p>Example: 2x + 3y = 6<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Subtract 2x : 3y = \u22122x + 6<\/li>\n\n\n\n<li>Divide by 3: y = \u22122\/3 x + 2<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope m =\u22122\/3<\/li>\n\n\n\n<li>Y-intercept b =2 \u2192 Point (0, 2)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-8938b15879773173fa1e1a844e413756\" style=\"color:#000060\"><strong>Graphing Using Slope and Y-Intercept<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Plot the y-intercept (0,b) on the graph.<\/li>\n\n\n\n<li>Use the slope m = rise\/runm to find another point.<\/li>\n\n\n\n<li>Draw the line through the points.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-c9214f249a2226213b64441f338b6e9f\" style=\"color:#000060\"><strong>Quick Tips<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always check if the equation is in y = mx + b form first.<\/li>\n\n\n\n<li>Slope is <strong>change in y \/ change in x<\/strong>.<\/li>\n\n\n\n<li>The y-intercept is <strong>just the constant term<\/strong> in slope-intercept form.<\/li>\n\n\n\n<li>A line can be drawn with just mmm and bbb.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-a623de198676c392481c0d3bcd20909c\" style=\"color:#000060\">\u2705 <strong>Example Practice<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>y = \u22123x + 4 \u2192 m = \u22123, b = 4<\/li>\n\n\n\n<li>5x \u2212 y = 10 \u2192 Rewrite: y = 5x \u2212 10 \u2192 m = 5, b = \u221210<\/li>\n<\/ul>\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<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#aee6ea\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-ca500a28476e8d027e2de159622f54bd\" style=\"color:#b00012\"><strong>Find the&nbsp;<em>y<\/em>-intercept of the following equation. Simplify your answer.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><em>y<\/em>&nbsp;= 2<em>x<\/em>&nbsp;\u2212 8<\/p>\n<\/div><\/div>\n\n\n\n<p>The y-intercept is on the y-axis, where x = 0. Plug x = 0 into the equation and solve for y.<\/p>\n\n\n\n<p>y = 2x \u2212 8<\/p>\n\n\n\n<p>y = 2(0) \u2212 8 <\/p>\n\n\n\n<p>y = \u20138    Simplify<\/p>\n\n\n\n<p>The <strong>y<\/strong>-intercept is   \u2013 8.<\/p>\n\n\n\n<p>Since the equation is in slope-intercept form (y = mx + b), you can also find the y-intercept by looking for b, the y-intercept.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y = 2x + \u20138<\/p>\n\n\n\n<p>Again,they-intercept is\u20138.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f4bbfc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-2971d2ff007ab2c0f6866736c18cb03f\" style=\"color:#b00012\"><strong>Find the slope of the line y = 9\/2 x + 1\/2<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Find the slope, m:<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y =9\/2 x + 1\/2<\/p>\n\n\n\n<p>The slope is 9\/2.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#dbe99f\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-ca500a28476e8d027e2de159622f54bd\" style=\"color:#b00012\"><strong>Find the&nbsp;<em>y<\/em>-intercept of the following equation. Simplify your answer.<\/strong><\/p>\n\n\n\n<p><em>y<\/em>&nbsp;= 6<em>x<\/em>&nbsp;+ 5<\/p>\n\n\n\n<p><em>y<\/em>-intercept =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>The y-intercept is on the y-axis, where x = 0. Plug x = 0 into the equation and solve for y.<\/p>\n\n\n\n<p>y = 6x + 5<\/p>\n\n\n\n<p>y = 6(0) + 5        Plugin x = 0<\/p>\n\n\n\n<p>y = 5               Simplify<\/p>\n\n\n\n<p>The &#8211; intercept is 5.<\/p>\n\n\n\n<p>Since the equation is in&nbsp;slope-intercept&nbsp;form&nbsp;(<em>y<\/em>&nbsp;= m<em>x<\/em>&nbsp;+ b), you can also find the&nbsp;<em>y<\/em>-intercept&nbsp;by looking for b, the&nbsp;<em>y<\/em>-intercept.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y = 6x + 5<\/p>\n\n\n\n<p>Again, they &#8211; intercept is 5.<\/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\/77923\/646\/711\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-113.png\" alt=\"\" class=\"wp-image-8039\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-113.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-113-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-113-150x150.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\/76848\/593\/965\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-122.png\" alt=\"\" class=\"wp-image-8040\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-122.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-122-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-122-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Slope-intercept form: find the slope and y-intercept T.5 Slope-intercept form: find the slope and y-intercept by Delta publications Key Notes: Definition The slope-intercept form of a linear equation is: y = mx + b Where: Understanding the Slope (m) m = y2 \u2212 y1 \/ x2 \u2212 x1 Understanding the Y-Intercept (b) Steps to Find<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-5-slope-intercept-form-find-the-slope-and-y-intercept\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.5 Slope-intercept form: find the slope and y-intercept&#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-307","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/307","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=307"}],"version-history":[{"count":26,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/307\/revisions"}],"predecessor-version":[{"id":17527,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/307\/revisions\/17527"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}