{"id":271623,"date":"2025-07-26T05:21:14","date_gmt":"2025-07-26T05:21:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271623"},"modified":"2025-07-26T05:21:16","modified_gmt":"2025-07-26T05:21:16","slug":"examine-the-graph-of-line-overleftrightarrow-ab-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/examine-the-graph-of-line-overleftrightarrow-ab-below\/","title":{"rendered":"Examine the graph of line overleftrightarrow AB below"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-733.png\" alt=\"\" class=\"wp-image-271624\"\/><\/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><strong>Correct Answer:<\/strong><br>y = -2\/3x + 2<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>To find the equation of the line, we can use the slope-intercept form, which is y = mx + b. In this formula, &#8216;m&#8217; represents the slope of the line, and &#8216;b&#8217; represents the y-intercept. The process involves finding these two values from the provided graph.<\/p>\n\n\n\n<p>First, we identify the y-intercept, &#8216;b&#8217;. This is the point where the line crosses the vertical y-axis. By examining the graph, we can see the line intersects the y-axis at the point (0, 2). Therefore, the value of the y-intercept, b, is 2.<\/p>\n\n\n\n<p>Next, we need to calculate the slope, &#8216;m&#8217;. The slope is a measure of the line&#8217;s steepness and is defined as the &#8216;rise&#8217; (vertical change) divided by the &#8216;run&#8217; (horizontal change) between any two points on the line. We can use the two labeled points, A at (-2, 3) and B at (4, -1), to calculate this.<\/p>\n\n\n\n<p>Using the slope formula, m = (y2 &#8211; y1) \/ (x2 &#8211; x1), we substitute the coordinates of points A and B:<br>m = (-1 &#8211; 3) \/ (4 &#8211; (-2))<br>m = -4 \/ (4 + 2)<br>m = -4 \/ 6<\/p>\n\n\n\n<p>This fraction simplifies to -2\/3. So, the slope &#8216;m&#8217; is -2\/3.<\/p>\n\n\n\n<p>Alternatively, we can find the slope by counting units on the grid. Starting from a clear point like the y-intercept (0, 2), we can observe that to get to the next clear point at (3, 0), we must move down 2 units (a rise of -2) and to the right 3 units (a run of +3). This gives a slope of rise over run, or -2\/3, confirming our calculation.<\/p>\n\n\n\n<p>With both the slope and y-intercept identified, we can now write the final equation. We substitute m = -2\/3 and b = 2 into the slope-intercept format y = mx + b. This gives us the complete equation for the line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2078.jpeg\" alt=\"\" class=\"wp-image-271625\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: Correct Answer:y = -2\/3x + 2 Explanation: To find the equation of the line, we can use the slope-intercept form, which is y = mx + b. In this formula, &#8216;m&#8217; represents the slope of the line, and &#8216;b&#8217; represents the y-intercept. The process involves finding these two values [&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-271623","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271623","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=271623"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271623\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}