{"id":233861,"date":"2025-06-13T13:20:38","date_gmt":"2025-06-13T13:20:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233861"},"modified":"2025-06-13T13:20:40","modified_gmt":"2025-06-13T13:20:40","slug":"what-is-the-equation-of-the-following-line-written-11-2x-y-1-0","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/what-is-the-equation-of-the-following-line-written-11-2x-y-1-0\/","title":{"rendered":"What is the equation of the following line written (1,1) 2x – y – 1 = 0"},"content":{"rendered":"\n

What is the equation of the following line written (1,1) 2x – y – 1 = 0<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Of course. Here is the solution and a detailed explanation.<\/p>\n\n\n\n

Correct Answer:<\/strong>
The equation of the line is 2x – y – 1 = 0<\/strong>.<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

To determine the equation of a line from its graph, one must first find its fundamental properties: the slope and a point on the line. The equation can then be constructed using these properties.<\/p>\n\n\n\n

Step 1: Finding the Slope of the Line<\/strong><\/p>\n\n\n\n

The slope, often denoted by the variable m<\/em>, measures the steepness of a line. It is calculated as the “rise” (the vertical change) divided by the “run” (the horizontal change) between any two distinct points on the line. The formula for the slope is:<\/p>\n\n\n\n

m<\/em> = (y\u2082 – y\u2081) \/ (x\u2082 – x\u2081)<\/p>\n\n\n\n

From the graph, we can identify two points where the line intersects the grid perfectly:<\/p>\n\n\n\n

    \n
  1. The point explicitly labeled:\u00a0(1, 1)<\/strong><\/li>\n\n\n\n
  2. The point where the line crosses the y-axis (the y-intercept):\u00a0(0, -1)<\/strong><\/li>\n<\/ol>\n\n\n\n

    Let (x\u2081, y\u2081) be (0, -1) and (x\u2082, y\u2082) be (1, 1). Now, substitute these values into the slope formula:<\/p>\n\n\n\n

    m<\/em> = (1 – (-1)) \/ (1 – 0)
    m<\/em> = (1 + 1) \/ 1
    m<\/em> = 2 \/ 1
    m<\/em> = 2<\/p>\n\n\n\n

    The slope of the line is 2.<\/p>\n\n\n\n

    Step 2: Using the Slope-Intercept Form<\/strong><\/p>\n\n\n\n

    The slope-intercept form of a linear equation is y = mx + b<\/strong>, where m<\/em> is the slope and b<\/em> is the y-intercept.<\/p>\n\n\n\n

    From Step 1, we found the slope m<\/em> = 2.
    The y-intercept is the point where the line crosses the y-axis. As identified from the graph, this occurs at (0, -1), so b<\/em> = -1.<\/p>\n\n\n\n

    Substituting these values into the slope-intercept form gives:
    y = 2x + (-1)
    y = 2x – 1<\/strong><\/p>\n\n\n\n

    Step 3: Converting to Standard Form<\/strong><\/p>\n\n\n\n

    The answer options are provided in the standard form of a linear equation, which is Ax + By + C = 0<\/strong>. To convert our equation (y = 2x – 1) into this format, we rearrange the terms so that they are all on one side of the equation.<\/p>\n\n\n\n

    Starting with y = 2x – 1, we can subtract y<\/em> from both sides:
    0 = 2x – y – 1<\/p>\n\n\n\n

    By convention, this is written as:
    2x – y – 1 = 0<\/strong><\/p>\n\n\n\n

    This matches the given option. To verify, we can substitute the point (1, 1) into this equation:
    2(1) – (1) – 1 = 0
    2 – 1 – 1 = 0
    0 = 0
    Since the equation holds true, it correctly represents the graphed line.thumb_upthumb_down<\/p>\n\n\n\n

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

    What is the equation of the following line written (1,1) 2x – y – 1 = 0 The Correct Answer and Explanation is: Of course. Here is the solution and a detailed explanation. Correct Answer:The equation of the line is 2x – y – 1 = 0. Explanation To determine the equation of a line from […]<\/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-233861","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233861","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=233861"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233861\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233861"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}