{"id":242157,"date":"2025-07-04T06:18:43","date_gmt":"2025-07-04T06:18:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242157"},"modified":"2025-07-04T06:18:45","modified_gmt":"2025-07-04T06:18:45","slug":"the-graph-of-linear-function-g-passes-through-the-points-7-4-and-7-6-as-shown","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/the-graph-of-linear-function-g-passes-through-the-points-7-4-and-7-6-as-shown\/","title":{"rendered":"The graph of linear function g passes through the points (-7, -4) and (7, 6), as shown."},"content":{"rendered":"\n<p>The graph of linear function g passes through the points (-7, -4) and (7, 6), as shown. What are the slope and y-intercept of the graph of g? A The slope is<\/p>\n\n\n\n<p>, and the y-intercept is -1. B The slope is<\/p>\n\n\n\n<p>, and the y-intercept is 1.<\/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\/image-98.png\" alt=\"\" class=\"wp-image-242163\"\/><\/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>The correct answer is&nbsp;<strong>B The slope is 5\/7, and the y-intercept is 1.<\/strong><\/p>\n\n\n\n<p>Here is a detailed explanation of how to determine the slope and y-intercept for the linear function g.<\/p>\n\n\n\n<p><strong>Finding the Slope<\/strong><\/p>\n\n\n\n<p>The slope of a line measures its steepness and is often described as &#8220;rise over run&#8221;. We can find the slope in two ways: by using the coordinates of the two given points or by observing the rise and run directly from the graph.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Using the Slope Formula:<\/strong>\u00a0The formula for the slope (m) of a line that passes through two points (x\u2081, y\u2081) and (x\u2082, y\u2082) is m = (y\u2082 &#8211; y\u2081) \/ (x\u2082 &#8211; x\u2081). The problem provides the points (-7, -4) and (7, 6). Let&#8217;s substitute these values into the formula:\n<ul class=\"wp-block-list\">\n<li>m = (6 &#8211; (-4)) \/ (7 &#8211; (-7))<\/li>\n\n\n\n<li>m = (6 + 4) \/ (7 + 7)<\/li>\n\n\n\n<li>m = 10 \/ 14<\/li>\n\n\n\n<li>Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2, gives us m = 5\/7.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Using the Graph (Rise over Run):<\/strong>\u00a0To find the slope from the graph, we can count the vertical change (rise) and the horizontal change (run) between the two points.\n<ul class=\"wp-block-list\">\n<li><strong>Rise:<\/strong>\u00a0Starting from the point (-7, -4), we move vertically upwards to be on the same horizontal level as the second point (7, 6). The change in the y-value is from -4 to 6, which is a total rise of 10 units.<\/li>\n\n\n\n<li><strong>Run:<\/strong>\u00a0From that new position, we move horizontally to the right to reach the point (7, 6). The change in the x-value is from -7 to 7, which is a total run of 14 units.<\/li>\n\n\n\n<li>The slope is the rise divided by the run, so m = 10\/14, which simplifies to 5\/7.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><strong>Finding the y-intercept<\/strong><\/p>\n\n\n\n<p>The y-intercept is the point where the line crosses the vertical y-axis. At this point, the x-coordinate is always zero.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Reading from the Graph:<\/strong>\u00a0By looking at the provided graph, we can visually identify where the line intersects the y-axis. The line passes through the y-axis at the value y = 1. Therefore, the y-intercept is 1.<\/li>\n\n\n\n<li><strong>Using the Slope-Intercept Equation:<\/strong>\u00a0The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We have already calculated the slope as 5\/7. We can now use one of the given points, such as (7, 6), and substitute the values of x, y, and m into the equation to solve for b.\n<ul class=\"wp-block-list\">\n<li>y = mx + b<\/li>\n\n\n\n<li>6 = (5\/7)(7) + b<\/li>\n\n\n\n<li>6 = 5 + b<\/li>\n\n\n\n<li>Subtracting 5 from both sides gives us b = 1.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>Both methods confirm that the slope is 5\/7 and the y-intercept is 1, which corresponds to option B.<\/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-banner5-217.jpeg\" alt=\"\" class=\"wp-image-242165\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The graph of linear function g passes through the points (-7, -4) and (7, 6), as shown. What are the slope and y-intercept of the graph of g? A The slope is , and the y-intercept is -1. B The slope is , and the y-intercept is 1. The Correct Answer and Explanation is: The [&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-242157","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242157","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=242157"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242157\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}