{"id":160362,"date":"2024-11-02T19:18:26","date_gmt":"2024-11-02T19:18:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=160362"},"modified":"2024-11-02T19:18:29","modified_gmt":"2024-11-02T19:18:29","slug":"which-is-the-graph-of-the-equation-y%e2%88%9212-3x%e2%88%923","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/02\/which-is-the-graph-of-the-equation-y%e2%88%9212-3x%e2%88%923\/","title":{"rendered":"Which is the graph of the equation y\u22121=2\/3(x\u22123)"},"content":{"rendered":"\n<p>Which is the graph of the equation y\u22121=2\/3(x\u22123)?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To graph the equation ( y &#8211; 1 = \\frac{2}{3}(x &#8211; 3) ), we start by rewriting it in the slope-intercept form, ( y = mx + b ). Here\u2019s how we can do that step by step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Distributing the Slope<\/strong>: We start with the equation in point-slope form:<br>[<br>y &#8211; 1 = \\frac{2}{3}(x &#8211; 3)<br>]<br>Next, we distribute ( \\frac{2}{3} ) on the right side:<br>[<br>y &#8211; 1 = \\frac{2}{3}x &#8211; 2<br>]<\/li>\n\n\n\n<li><strong>Isolating ( y )<\/strong>: To isolate ( y ), we add ( 1 ) to both sides:<br>[<br>y = \\frac{2}{3}x &#8211; 2 + 1<br>]<br>Simplifying this gives:<br>[<br>y = \\frac{2}{3}x &#8211; 1<br>]<br>Now, we can see that the slope ( m ) is ( \\frac{2}{3} ) and the y-intercept ( b ) is ( -1 ).<\/li>\n\n\n\n<li><strong>Plotting the Graph<\/strong>: With the slope and y-intercept, we can plot the graph:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start at the y-intercept ((0, -1)).<\/li>\n\n\n\n<li>From this point, use the slope ( \\frac{2}{3} ) to find another point. This means that for every 3 units you move to the right (positive direction along the x-axis), you move up 2 units (positive direction along the y-axis).<\/li>\n\n\n\n<li>From ((0, -1)), moving 3 units to the right takes you to ( (3, -1) ), and then moving up 2 units brings you to ( (3, 1) ).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finalizing the Line<\/strong>: Draw a line through the points ( (0, -1) ) and ( (3, 1) ). This line extends infinitely in both directions.<\/li>\n\n\n\n<li><strong>Additional Points<\/strong>: For further accuracy, you could find additional points by substituting other x-values into the equation.<\/li>\n<\/ol>\n\n\n\n<p>Thus, the graph of the equation ( y &#8211; 1 = \\frac{2}{3}(x &#8211; 3) ) is a straight line with a slope of ( \\frac{2}{3} ) and a y-intercept at (-1).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which is the graph of the equation y\u22121=2\/3(x\u22123)? The Correct Answer and Explanation is: To graph the equation ( y &#8211; 1 = \\frac{2}{3}(x &#8211; 3) ), we start by rewriting it in the slope-intercept form, ( y = mx + b ). Here\u2019s how we can do that step by step: Thus, the graph [&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-160362","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160362","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=160362"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160362\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}