{"id":278209,"date":"2025-08-01T20:49:54","date_gmt":"2025-08-01T20:49:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278209"},"modified":"2025-08-01T20:49:56","modified_gmt":"2025-08-01T20:49:56","slug":"which-relationship-has-a-zero-slope","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/01\/which-relationship-has-a-zero-slope\/","title":{"rendered":"Which relationship has a zero slope"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The correct answer is the table on the top left.<\/p>\n\n\n\n

A zero slope is a fundamental concept in algebra that describes a specific type of linear relationship. The slope of a line, often represented by the variable ‘m’, measures its steepness and direction. It is calculated as the “rise” divided by the “run,” or the change in the vertical direction (y-axis) for every unit of change in the horizontal direction (x-axis). The formula for slope is m = (y\u2082 – y\u2081) \/ (x\u2082 – x\u2081), where (x\u2081, y\u2081) and (x\u2082, y\u2082) are any two points on the line.<\/p>\n\n\n\n

For a relationship to have a zero slope, the numerator of this formula, (y\u2082 – y\u2081), must be equal to zero. This happens only when the y-value does not change, meaning y\u2082 = y\u2081. In other words, a relationship has a zero slope if the y-coordinate remains constant for all x-coordinates. Graphically, this creates a perfectly horizontal line.<\/p>\n\n\n\n

Let’s analyze the given options based on this understanding.<\/p>\n\n\n\n

The first table, located at the top left, shows the points (-3, 2), (-1, 2), (1, 2), and (3, 2). In this relationship, the y-value is always 2, regardless of the x-value. Calculating the slope using any two points, for instance (-1, 2) and (3, 2), gives us m = (2 – 2) \/ (3 – (-1)) = 0 \/ 4 = 0. Therefore, this relationship has a zero slope.<\/p>\n\n\n\n

The other options are incorrect. The second table has changing y-values, resulting in a non-zero slope (specifically, -1). The graph on the top right shows a diagonal line that rises from left to right, indicating a positive slope. The graph on the bottom left shows a vertical line. A vertical line has an undefined slope, not a zero slope, because the x-value is constant, which leads to division by zero in the slope formula.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

The correct answer is the table on the top left. A zero slope is a fundamental concept in algebra that describes a specific type of linear relationship. The slope of a line, often represented by the variable ‘m’, measures its steepness and direction. It is calculated as the “rise” divided by the “run,” or the […]<\/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-278209","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278209","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=278209"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278209\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}