{"id":311,"date":"2022-04-13T09:01:19","date_gmt":"2022-04-13T09:01:19","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=311"},"modified":"2025-08-13T05:36:37","modified_gmt":"2025-08-13T05:36:37","slug":"t-7-slope-intercept-form-write-an-equation-from-a-graph","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-7-slope-intercept-form-write-an-equation-from-a-graph\/","title":{"rendered":"T.7 Slope-intercept form: write an equation from a graph"},"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 from a graph<\/strong><\/h2>\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-e8963a3659ed52b5cb2506288a3a9b8a\" style=\"color:#000060\"><strong>Understanding Slope-Intercept Form<\/strong><\/h3>\n\n\n\n<p>The slope-intercept form 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> = slope (rate of change)<\/li>\n\n\n\n<li><strong>b<\/strong> = y-intercept (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-0ece01d64d64a3680ca4995647872393\" style=\"color:#000060\"><strong>Identifying the Slope (m) from a Graph<\/strong><\/h3>\n\n\n\n<p><strong>Slope formula<\/strong>: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>m=rise \/ runm <\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rise<\/strong> = vertical change (difference in y-values)<\/li>\n\n\n\n<li><strong>Run<\/strong> = horizontal change (difference in x-values)<\/li>\n<\/ul>\n\n\n\n<p>Steps to find slope:<ol><li>Pick <strong>two points<\/strong> on the line (make sure they are exact grid points).<\/li><li>Count how many units you move <strong>up\/down<\/strong> (rise) and <strong>left\/right<\/strong> (run).<\/li><li>Divide rise by run.<\/li><\/ol><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Positive slope \u2192 line goes <strong>up<\/strong> from left to right.<\/li>\n\n\n\n<li>Negative slope \u2192 line goes <strong>down<\/strong> from left to right.<\/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-dbf7054bb19017ac5794a635ba5754b1\" style=\"color:#000060\"><strong>Finding the y-Intercept (b)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Locate the point where the line crosses the <strong>y &#8211; axis<\/strong>.<\/li>\n\n\n\n<li>The y-coordinate of this point is <strong>b<\/strong>.<\/li>\n\n\n\n<li>Example: If the line crosses at (0, 4), then <strong>b = 4<\/strong>.<\/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-87bd5a892a140365403ba6bfc5aa3244\" style=\"color:#000060\"><strong>Writing the Equation<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Write the general slope-intercept form: y = mx + b.<\/li>\n\n\n\n<li>Substitute <strong>m<\/strong> and <strong>b<\/strong> with the values from the graph.<\/li>\n\n\n\n<li>Simplify if needed.<\/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-8c705e1662000538b261543f7ab2b300\" style=\"color:#000060\"><strong>Example<\/strong><\/h3>\n\n\n\n<p>From the graph:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Line passes through points (0, 2) and (3, 5).<\/li>\n\n\n\n<li>Slope: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>m=5\u22122 \/ 3\u22120 = 3 \/ 3=1<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>y-intercept: <strong>b = 2<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Equation: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y = 1x + 2 or y = x + 2<\/strong><\/p>\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-de701b1532fc263cf992238246298415\" style=\"color:#000060\"><strong>Tips<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always choose points where the grid lines meet exactly.<\/li>\n\n\n\n<li>Check the slope sign carefully (positive or negative).<\/li>\n\n\n\n<li>If the line is horizontal: m=0 \u2192 equation is y=b.<\/li>\n\n\n\n<li>If the line is vertical: slope is undefined \u2192 equation is x=a (not in slope-intercept form).<\/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-background-background-color has-text-color has-background has-link-color has-large-font-size wp-elements-69ca32a715aaad77b8ecfeb200a25dca\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#939ce3\"><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-background-background-color has-background\">Look at this graph<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\"><div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-15.png\" alt=\"\" class=\"wp-image-11574\" style=\"width:464px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-9ec65194684122c10a0011c05bc8f65e\" style=\"color:#b00012\"><strong>What is the equation of the line in slope-intercept form?<\/strong><\/p>\n\n\n\n<p class=\"has-background-background-color has-background\">solution:<\/p>\n\n\n\n<p class=\"has-background-background-color has-background\">First, find the slope m. Pick two points on the line, such as&nbsp;(0,&nbsp;3)&nbsp;and&nbsp;(7,&nbsp;4). Plug those points into the slope formula.<\/p>\n\n\n\n<p><strong>m= change in&nbsp;<em>y<\/em>\/change in&nbsp;x<\/strong><\/p>\n\n\n\n<p>m = 4-3\/7-0<\/p>\n\n\n\n<p>m = 1\/7<\/p>\n\n\n\n<p>The slope is =1\/7<\/p>\n\n\n\n<p>Now find the&nbsp;<em>y<\/em>-intercept. Since the line crosses the&nbsp;<em>y<\/em>-axis&nbsp;at 3, the&nbsp;<em>y<\/em>-intercept&nbsp;is 3.<\/p>\n\n\n\n<p>Finally, use the slope m =1\/7 and the y-intercept b = 3 to write the equation in slope-intercept form.<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><em>y<\/em>&nbsp;=&nbsp;m<em>x<\/em>&nbsp;+ b<\/p>\n\n\n\n<p class=\"has-text-align-center has-foreground-color has-text-color has-huge-font-size\"><strong>y =1\/7x + 3<\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#e18294\"><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>Look at this graph.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-18.png\" alt=\"\" class=\"wp-image-11580\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4fc705b40fa1f4b1c90f5efa189ef7b4\" style=\"color:#b00012\"><strong>What is the equation of the line in slope-intercept form?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First find the slope m. Pick two points on the line, such as&nbsp;(0,&nbsp;-2)&nbsp;and&nbsp;(1,&nbsp;0). Plug those points into the slope formula.<\/p>\n\n\n\n<p>m = change in y \/ change in x<\/p>\n\n\n\n<p>m = 0 &#8211; -2 \/ 1 &#8211; 0          Plugin&nbsp;(<strong>0<\/strong>,&nbsp;<strong>-2<\/strong>)&nbsp;and&nbsp;(<strong>1<\/strong>,&nbsp;<strong>0<\/strong>)<\/p>\n\n\n\n<p>m = 2\/1                   Simplify<\/p>\n\n\n\n<p>m = 2                 Simplify<\/p>\n\n\n\n<p>The slope is 2.<\/p>\n\n\n\n<p>Now find the&nbsp;<em>y<\/em>-intercept. Since the line crosses the&nbsp;<em>y<\/em>-axis&nbsp;at&nbsp;-2, the&nbsp;<em>y<\/em>-intercept&nbsp;is&nbsp;-2.<\/p>\n\n\n\n<p>Finally, use the slope m = 2 and the y-intercept b = 2 to write the equation in slope-intercept form.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y = 2x + \u20132              Plugin m=2 and b = \u20132<\/p>\n\n\n\n<p>y = 2x \u2212 2             Rewrite as subtraction<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#92f0b3\"><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>Look at this graph.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-17.png\" alt=\"\" class=\"wp-image-11578\" style=\"width:422px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-9ec65194684122c10a0011c05bc8f65e\" style=\"color:#b00012\"><strong>What is the equation of the line in slope-intercept form?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First find the slope m. Pick two points on the line, such as (0, 10) and (1, 5). Plug those points into the slope formula.<\/p>\n\n\n\n<p>m =change in y\/ change in x<\/p>\n\n\n\n<p>m =5 \u2212 10 \/1 \u2212 0 Plugin (0, 10) and (1, 5)<\/p>\n\n\n\n<p>m =\u20135\/1      Simplify<\/p>\n\n\n\n<p>m = \u20135        Simplify<\/p>\n\n\n\n<p>Theslopeis\u20135.<\/p>\n\n\n\n<p>Now find the y-intercept. Since the line crosses the y-axis at 10, the y-intercept is 10.<\/p>\n\n\n\n<p>Finally,usetheslopem = \u20135andthey-interceptb = 10towritetheequationinslope-interceptform.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y = \u20135x + 10 Plugin m = \u20135 and b = 10<\/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\/77926\/452\/649\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-111.png\" alt=\"\" class=\"wp-image-8033\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-111.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-111-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-111-150x150.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\/76979\/540\/422\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-120.png\" alt=\"\" class=\"wp-image-8034\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-120.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-120-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-120-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Slope-intercept form: write an equation from a graph Key Notes: Understanding Slope-Intercept Form The slope-intercept form of a linear equation is: y = mx + b where: Identifying the Slope (m) from a Graph Slope formula: m=rise \/ runm Steps to find slope: Pick two points on the line (make sure they are exact grid<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-7-slope-intercept-form-write-an-equation-from-a-graph\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.7 Slope-intercept form: write an equation from a graph&#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-311","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/311","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=311"}],"version-history":[{"count":22,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/311\/revisions"}],"predecessor-version":[{"id":17454,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/311\/revisions\/17454"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}