{"id":67,"date":"2022-04-13T09:53:53","date_gmt":"2022-04-13T09:53:53","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=67"},"modified":"2025-03-05T07:05:40","modified_gmt":"2025-03-05T07:05:40","slug":"d-7-slope-intercept-form-write-an-equation-from-a-graph","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/d-7-slope-intercept-form-write-an-equation-from-a-graph\/","title":{"rendered":"D.7 Slope-intercept form: write an equation from a graph"},"content":{"rendered":"\n

Slope-intercept form: write an equation from a graph<\/strong><\/h2>\n\n\n\n

Key Notes:<\/p>\n\n\n\n

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The slope-intercept form<\/strong> of a linear equation is<\/p>\n\n\n\n

y<\/em> = mx<\/em> + b<\/p>\n\n\n\n

where m is the slope and b is the y-intercept.<\/p>\n\n\n\n

The slope formula is m= change in y<\/em>\/change in x<\/strong><\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

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Look at this graph<\/p>\n\n\n\n

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\"\"<\/figure><\/div>\n\n\n

What is the equation of the line in slope-intercept form?<\/strong><\/p>\n\n\n\n

solution:<\/p>\n\n\n\n

First, find the slope m. Pick two points on the line, such as (0, 3) and (7, 4). Plug those points into the slope formula.<\/p>\n\n\n\n

m= change in y<\/em>\/change in x<\/strong><\/p>\n\n\n\n

m = 4-3\/7-0<\/p>\n\n\n\n

m = 1\/7<\/p>\n\n\n\n

The slope is =1\/7<\/p>\n\n\n\n

Now find the y<\/em>-intercept. Since the line crosses the y<\/em>-axis at 3, the y<\/em>-intercept is 3.<\/p>\n\n\n\n

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

y<\/em> = mx<\/em> + b<\/p>\n\n\n\n

y =1\/7x + 3<\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n

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Look at this graph.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the equation of the line in slope-intercept form?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

First find the slope m. Pick two points on the line, such as (0, -2) and (1, 0). Plug those points into the slope formula.<\/p>\n\n\n\n

m = change in y \/ change in x<\/p>\n\n\n\n

m = 0 – -2 \/ 1 – 0 Plugin (0<\/strong>, -2<\/strong>) and (1<\/strong>, 0<\/strong>)<\/p>\n\n\n\n

m = 2\/1 Simplify<\/p>\n\n\n\n

m = 2 Simplify<\/p>\n\n\n\n

The slope is 2.<\/p>\n\n\n\n

Now find the y<\/em>-intercept. Since the line crosses the y<\/em>-axis at -2, the y<\/em>-intercept is -2.<\/p>\n\n\n\n

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

y = mx + b<\/p>\n\n\n\n

y = 2x + \u20132 Plugin m=2 and b = \u20132<\/p>\n\n\n\n

y = 2x \u2212 2 Rewrite as subtraction<\/p>\n<\/div><\/div>\n\n\n\n

\n
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Look at this graph.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the equation of the line in slope-intercept form?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

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

m =change in y\/ change in x<\/p>\n\n\n\n

m =5 \u2212 10 \/1 \u2212 0 Plugin (0, 10) and (1, 5)<\/p>\n\n\n\n

m =\u20135\/1 Simplify<\/p>\n\n\n\n

m = \u20135 Simplify<\/p>\n\n\n\n

Theslopeis\u20135.<\/p>\n\n\n\n

Now find the y-intercept. Since the line crosses the y-axis at 10, the y-intercept is 10.<\/p>\n\n\n\n

Finally,usetheslopem = \u20135andthey-interceptb = 10towritetheequationinslope-interceptform.<\/p>\n\n\n\n

y = mx + b<\/p>\n\n\n\n

y = \u20135x + 10 Plugin m = \u20135 and b = 10<\/p>\n<\/div><\/div>\n\n\n\n

Let’s Practice!<\/p>\n<\/div><\/div>\n\n\n\n

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\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Slope-intercept form: write an equation from a graph Key Notes: The slope-intercept form of a linear equation is y = mx + b where m is the slope and b is the y-intercept. The slope formula is m= change in y\/change in x Learn with an example Look at this graph What is the equation of the line in slope-intercept form? solution:Continue reading “D.7 Slope-intercept form: write an equation from a graph”<\/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-67","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=67"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/67\/revisions"}],"predecessor-version":[{"id":17587,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/67\/revisions\/17587"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}