{"id":220884,"date":"2025-05-29T03:22:27","date_gmt":"2025-05-29T03:22:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220884"},"modified":"2025-05-29T03:22:30","modified_gmt":"2025-05-29T03:22:30","slug":"y-1-4x-y-15-2x-y-15-7x-y-10-7x-y-10-slope-intercept-form-slope-m-y-intercept-b-a-b-c-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/29\/y-1-4x-y-15-2x-y-15-7x-y-10-7x-y-10-slope-intercept-form-slope-m-y-intercept-b-a-b-c-3\/","title":{"rendered":"y = -1 4x + y = 15 -2x + y = 15 7x + y = 10 7x + y = 10 Slope Intercept Form Slope (m) Y-Intercept (b) A B C 3"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-498.png\" alt=\"\" class=\"wp-image-220885\"\/><\/figure>\n\n\n\n<p>y = -1 4x + y = 15 -2x + y = 15 7x + y = 10 7x + y = 10 Slope Intercept Form Slope (m) Y-Intercept (b) A B C 3<br><br><\/p>\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>Let&#8217;s solve the table row by row. To convert a linear equation to <strong>slope-intercept form<\/strong> (i.e., y=mx+by = mx + b), isolate yy on one side. Then identify the <strong>slope (m)<\/strong> and <strong>y-intercept (b)<\/strong>. For columns A, B, and C, we will determine whether the system of equations in each pair is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A (Same Line \/ Infinite Solutions)<\/strong><\/li>\n\n\n\n<li><strong>B (Parallel Lines \/ No Solution)<\/strong><\/li>\n\n\n\n<li><strong>C (Intersecting Lines \/ One Solution)<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Completed Table:<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>System of Linear Equation<\/th><th>Slope Intercept Form<\/th><th>Slope (m)<\/th><th>Y-Intercept (b)<\/th><th>A<\/th><th>B<\/th><th>C<\/th><\/tr><\/thead><tbody><tr><td>2x + y = 5<\/td><td>y = -2x + 5<\/td><td>-2<\/td><td>5<\/td><td><\/td><td><\/td><td><\/td><\/tr><tr><td>2x + y = 6<\/td><td>y = -2x + 6<\/td><td>-2<\/td><td>6<\/td><td><\/td><td>\u2714<\/td><td><\/td><\/tr><tr><td>-8x + y = -1<\/td><td>y = 8x &#8211; 1<\/td><td>8<\/td><td>-1<\/td><td><\/td><td><\/td><td><\/td><\/tr><tr><td>-8x + y = -1<\/td><td>y = 8x &#8211; 1<\/td><td>8<\/td><td>-1<\/td><td>\u2714<\/td><td><\/td><td><\/td><\/tr><tr><td>4x + y = 15<\/td><td>y = -4x + 15<\/td><td>-4<\/td><td>15<\/td><td><\/td><td><\/td><td><\/td><\/tr><tr><td>-2x + y = 15<\/td><td>y = 2x + 15<\/td><td>2<\/td><td>15<\/td><td><\/td><td><\/td><td>\u2714<\/td><\/tr><tr><td>7x + y = 10<\/td><td>y = -7x + 10<\/td><td>-7<\/td><td>10<\/td><td><\/td><td><\/td><td><\/td><\/tr><tr><td>7x + y = 10<\/td><td>y = -7x + 10<\/td><td>-7<\/td><td>10<\/td><td>\u2714<\/td><td><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u270d\ufe0f Explanation<\/h3>\n\n\n\n<p>This table analyzes systems of linear equations by converting them into <strong>slope-intercept form<\/strong>, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Understanding the slope and y-intercept helps determine the relationship between lines\u2014whether they are <strong>parallel, intersecting<\/strong>, or the <strong>same line<\/strong>.<\/p>\n\n\n\n<p>For example, the first pair:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>2x + y = 5<\/strong> and <strong>2x + y = 6<\/strong> both have the same slope m=\u22122m = -2, but different y-intercepts (5 and 6). This means the lines are <strong>parallel<\/strong>, so they never meet\u2014<strong>no solution (B)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>In the second pair:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>-8x + y = -1<\/strong> appears twice. When simplified, both become y=8x\u22121y = 8x &#8211; 1, which are <strong>identical lines<\/strong>. Therefore, they have <strong>infinitely many solutions (A)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>In the third pair:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>4x + y = 15<\/strong> becomes y=\u22124x+15y = -4x + 15, while <strong>-2x + y = 15<\/strong> becomes y=2x+15y = 2x + 15. The slopes are different, meaning the lines will intersect at one point\u2014<strong>one solution (C)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Finally, the last pair:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>7x + y = 10<\/strong> appears twice and simplifies to y=\u22127x+10y = -7x + 10. These are identical again, so there are <strong>infinitely many solutions (A)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>This analysis is crucial for solving systems of equations graphically or algebraically, especially in understanding whether solutions exist and how many.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner6-106.jpeg\" alt=\"\" class=\"wp-image-220886\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>y = -1 4x + y = 15 -2x + y = 15 7x + y = 10 7x + y = 10 Slope Intercept Form Slope (m) Y-Intercept (b) A B C 3 The Correct Answer and Explanation is: Let&#8217;s solve the table row by row. To convert a linear equation to slope-intercept form [&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-220884","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220884","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=220884"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220884\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}