{"id":242466,"date":"2025-07-04T07:44:03","date_gmt":"2025-07-04T07:44:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242466"},"modified":"2025-07-04T07:44:05","modified_gmt":"2025-07-04T07:44:05","slug":"8-6-2-5-8-6-2-5-2-6-8-8-6-8-6-2-2-6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/8-6-2-5-8-6-2-5-2-6-8-8-6-8-6-2-2-6\/","title":{"rendered":"8 6 2 5 8 6 2 5 -2 6 8 8 6 8 6 2 -2 6"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-107.png\" alt=\"\" class=\"wp-image-242472\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Here are the equations for each of the four graphed lines:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Top Left Graph:<\/strong>\u00a0y = -1\/2x &#8211; 2<\/li>\n\n\n\n<li><strong>Middle Left Graph:<\/strong>\u00a0y = -1\/2x + 2<\/li>\n\n\n\n<li><strong>Bottom Left Graph:<\/strong>\u00a0y = 1\/2x + 2<\/li>\n\n\n\n<li><strong>Middle Right Graph:<\/strong>\u00a0y = 1\/2x &#8211; 2<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>To determine the equation for each line, we use the slope-intercept form, which is written as y = mx + b. In this formula, &#8216;b&#8217; represents the y-intercept, which is the point where the line crosses the vertical y-axis. The variable &#8216;m&#8217; represents the slope of the line, which measures its steepness and direction. The slope is calculated as &#8220;rise over run,&#8221; or the change in the vertical position (y) divided by the change in the horizontal position (x) between any two points on the line.<\/p>\n\n\n\n<p>For the&nbsp;<strong>top left graph<\/strong>, the line intersects the y-axis at -2, so the y-intercept (b) is -2. To find the slope (m), we can select two clear points on the line, such as the y-intercept (0, -2) and another point, (4, -4). The vertical change, or rise, is from -2 to -4, which is a change of -2. The horizontal change, or run, is from 0 to 4, which is a change of +4. Therefore, the slope (m) is -2\/4, which simplifies to -1\/2. The line slopes downward from left to right, confirming the negative slope. The final equation is y = -1\/2x &#8211; 2.<\/p>\n\n\n\n<p>For the&nbsp;<strong>middle left graph<\/strong>, the line crosses the y-axis at +2, making the y-intercept (b) equal to 2. Using the y-intercept (0, 2) and another point on the line, (4, 0), we can calculate the slope. The rise is from 2 to 0, a change of -2, and the run is from 0 to 4, a change of +4. The slope (m) is -2\/4, which simplifies to -1\/2. The equation for this line is y = -1\/2x + 2.<\/p>\n\n\n\n<p>For the&nbsp;<strong>bottom left graph<\/strong>, the line\u2019s y-intercept (b) is also at +2. This line, however, slopes upward from left to right, indicating a positive slope. Using the points (0, 2) and (4, 4), we see the rise is from 2 to 4, which is +2, and the run is from 0 to 4, which is +4. The slope (m) is 2\/4, or 1\/2. The resulting equation is y = 1\/2x + 2.<\/p>\n\n\n\n<p>Finally, for the\u00a0<strong>middle right graph<\/strong>, the line intersects the y-axis at -2, so b = -2. This line also slopes upward, so we expect a positive slope. Let&#8217;s use the points (0, -2) and (4, 0). The rise is from -2 to 0 (+2), and the run is from 0 to 4 (+4). The slope (m) is 2\/4, which simplifies to 1\/2. Thus, the equation for this line is y = 1\/2x &#8211; 2. By systematically identifying the y-intercept and calculating the slope for each line, we can accurately determine its unique linear equation<\/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-banner8-120.jpeg\" alt=\"\" class=\"wp-image-242473\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: Here are the equations for each of the four graphed lines: To determine the equation for each line, we use the slope-intercept form, which is written as y = mx + b. In this formula, &#8216;b&#8217; represents the y-intercept, which is the point where the line crosses the vertical [&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-242466","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242466","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=242466"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242466\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242466"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242466"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}