{"id":233865,"date":"2025-06-13T13:24:21","date_gmt":"2025-06-13T13:24:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233865"},"modified":"2025-06-13T13:24:25","modified_gmt":"2025-06-13T13:24:25","slug":"select-the-graph-for-this-equation-by-using-slope-intercept-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/select-the-graph-for-this-equation-by-using-slope-intercept-form\/","title":{"rendered":"Select the graph for this equation by using slope-intercept form."},"content":{"rendered":"\n<p>Select the graph for this equation by using slope-intercept form.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-444.png\" alt=\"\" class=\"wp-image-233867\" style=\"width:959px;height:auto\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To select the correct graph for the equation&nbsp;2x + y = 1, it is essential to first convert the equation into slope-intercept form, which is written as&nbsp;<strong>y = mx + b<\/strong>. In this form,&nbsp;m&nbsp;represents the slope of the line, and&nbsp;b&nbsp;represents the y-intercept, which is the point where the line crosses the vertical y-axis.<\/p>\n\n\n\n<p><strong>Step 1: Convert the equation to slope-intercept form.<\/strong><\/p>\n\n\n\n<p>The given equation is&nbsp;2x + y = 1. To transform this into the&nbsp;y = mx + b&nbsp;format, the variable&nbsp;y&nbsp;must be isolated on one side of the equation. This is achieved by subtracting&nbsp;2x&nbsp;from both sides of the equation:<\/p>\n\n\n\n<p>2x &#8211; 2x + y = 1 &#8211; 2x<br>y = -2x + 1<\/p>\n\n\n\n<p>Now the equation is in slope-intercept form.<\/p>\n\n\n\n<p><strong>Step 2: Identify the slope (m) and the y-intercept (b).<\/strong><\/p>\n\n\n\n<p>By comparing&nbsp;y = -2x + 1&nbsp;to the general form&nbsp;y = mx + b, the following values can be identified:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The\u00a0<strong>y-intercept (b)<\/strong>\u00a0is\u00a0<strong>1<\/strong>. This means the line will cross the y-axis at the point (0, 1).<\/li>\n\n\n\n<li>The\u00a0<strong>slope (m)<\/strong>\u00a0is\u00a0<strong>-2<\/strong>. The slope indicates the steepness and direction of the line. It can be expressed as a fraction,\u00a0m = -2\/1, which represents the &#8220;rise over run.&#8221;<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 3: Use the y-intercept and slope to find points on the graph.<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Plot the y-intercept:<\/strong>\u00a0Begin by locating the y-intercept on the coordinate plane. Since\u00a0b = 1, the first point is at\u00a0<strong>(0, 1)<\/strong>.<\/li>\n\n\n\n<li><strong>Apply the slope:<\/strong>\u00a0The slope\u00a0m = -2\/1\u00a0provides directions to find a second point. The &#8220;rise&#8221; is -2, which means moving 2 units down. The &#8220;run&#8221; is 1, which means moving 1 unit to the right. Starting from the y-intercept (0, 1), move 2 units down and 1 unit to the right. This brings you to the point\u00a0<strong>(1, -1)<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>The correct graph is a straight line that passes through the points&nbsp;<strong>(0, 1)<\/strong>&nbsp;and&nbsp;<strong>(1, -1)<\/strong>. It will be a downward-sloping line that crosses the y-axis at a positive value.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-350.jpeg\" alt=\"\" class=\"wp-image-233868\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Select the graph for this equation by using slope-intercept form. The Correct Answer and Explanation is: To select the correct graph for the equation&nbsp;2x + y = 1, it is essential to first convert the equation into slope-intercept form, which is written as&nbsp;y = mx + b. In this form,&nbsp;m&nbsp;represents the slope of the line, [&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-233865","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233865","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=233865"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233865\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}