{"id":186512,"date":"2025-01-25T08:39:20","date_gmt":"2025-01-25T08:39:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186512"},"modified":"2025-01-25T08:39:22","modified_gmt":"2025-01-25T08:39:22","slug":"rewrite-the-given-equation-in-slope-intercept-form-and-then-graph-the-line","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/25\/rewrite-the-given-equation-in-slope-intercept-form-and-then-graph-the-line\/","title":{"rendered":"Rewrite the given equation in slope-intercept form and then graph the line"},"content":{"rendered":"\n<p>Rewrite the given equation in slope-intercept form and then graph the line. 7x + 5y &#8211; 35 = 0<br>What is the equation in slope-intercept form?<br>(Use integers or simplified fractions for any numbers in the equation.)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To rewrite the given equation ( 7x + 5y &#8211; 35 = 0 ) into slope-intercept form, we need to solve for ( y ). The slope-intercept form of a linear equation is written as:<\/p>\n\n\n\n<p>[<br>y = mx + b<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( m ) is the slope of the line, and<\/li>\n\n\n\n<li>( b ) is the y-intercept.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Solution:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Start with the original equation:<\/strong><br>[<br>7x + 5y &#8211; 35 = 0<br>]<\/li>\n\n\n\n<li><strong>Move all terms involving ( x ) and constants to one side by subtracting ( 7x ) and adding 35 to both sides:<\/strong><br>[<br>5y = -7x + 35<br>]<\/li>\n\n\n\n<li><strong>Now, solve for ( y ) by dividing the entire equation by 5:<\/strong><br>[<br>y = \\frac{-7x + 35}{5}<br>]<br>This can be simplified by splitting the fraction:<br>[<br>y = -\\frac{7}{5}x + 7<br>]<\/li>\n<\/ol>\n\n\n\n<p>So, the equation in slope-intercept form is:<br>[<br>y = -\\frac{7}{5}x + 7<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>slope<\/strong> ( m ) of the line is ( -\\frac{7}{5} ), which means for every 5 units you move to the right (increasing ( x )), the value of ( y ) decreases by 7 units. This negative slope indicates that the line falls as you move from left to right.<\/li>\n\n\n\n<li>The <strong>y-intercept<\/strong> ( b ) is 7, meaning the line crosses the y-axis at the point ( (0, 7) ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Graphing the Line:<\/h3>\n\n\n\n<p>To graph the equation ( y = -\\frac{7}{5}x + 7 ), you can start by plotting the y-intercept at ( (0, 7) ). Then, use the slope of ( -\\frac{7}{5} ) to plot another point. From ( (0, 7) ), move 5 units to the right (along the x-axis) and 7 units down (since the slope is negative). This gives you the point ( (5, 0) ). Drawing a line through these two points will give you the graph of the equation.<\/p>\n\n\n\n<p>This slope-intercept form is useful because it directly shows the slope and y-intercept, making it easy to graph and analyze the line.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rewrite the given equation in slope-intercept form and then graph the line. 7x + 5y &#8211; 35 = 0What is the equation in slope-intercept form?(Use integers or simplified fractions for any numbers in the equation.) The Correct Answer and Explanation is : To rewrite the given equation ( 7x + 5y &#8211; 35 = 0 [&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-186512","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186512","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=186512"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186512\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}