{"id":276166,"date":"2025-07-30T17:36:03","date_gmt":"2025-07-30T17:36:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=276166"},"modified":"2025-07-30T17:36:05","modified_gmt":"2025-07-30T17:36:05","slug":"the-table-gives-the-coordinates-of-two-points-on-a-line-in-the-xy-plane","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/30\/the-table-gives-the-coordinates-of-two-points-on-a-line-in-the-xy-plane\/","title":{"rendered":"The table gives the coordinates of two points on a line in the xy-plane"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Correct Answer: 33<\/strong><\/p>\n\n\n\n

To determine the value of b, we can use the fundamental property of a straight line: the slope between any two points on the line is constant. The problem provides us with three points that all lie on the same line: (k, 13), (k + 7, -15), and (k – 5, b).<\/p>\n\n\n\n

First, let’s calculate the slope of the line using the two points given in the table. Let the first point be (x\u2081, y\u2081) = (k, 13) and the second point be (x\u2082, y\u2082) = (k + 7, -15). The formula for the slope, denoted by m, is the change in y divided by the change in x.<\/p>\n\n\n\n

m = (y\u2082 – y\u2081) \/ (x\u2082 – x\u2081)
m = (-15 – 13) \/ ((k + 7) – k)<\/p>\n\n\n\n

Calculating the numerator and the denominator separately gives us:
Numerator: -15 – 13 = -28
Denominator: (k + 7) – k = 7<\/p>\n\n\n\n

Now, we can find the slope:
m = -28 \/ 7 = -4<\/p>\n\n\n\n

So, the slope of the line is -4.<\/p>\n\n\n\n

Next, since the point (k – 5, b) is also on this line, the slope between this point and any other point on the line must also be -4. Let’s use the first point from the table, (k, 13), and the third point, (k – 5, b).<\/p>\n\n\n\n

Using the slope formula again with these two points:
m = (b – 13) \/ ((k – 5) – k)<\/p>\n\n\n\n

The denominator simplifies to (k – 5 – k), which is -5. We can now set up an equation since we know the slope must be -4:
-4 = (b – 13) \/ -5<\/p>\n\n\n\n

To solve for b, we multiply both sides of the equation by -5:
(-4) * (-5) = b – 13
20 = b – 13<\/p>\n\n\n\n

Finally, we add 13 to both sides to isolate b:
20 + 13 = b
b = 33<\/p>\n\n\n\n

Therefore, the value of b is 33. This method works without needing to determine the specific value of the constant k.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: Correct Answer: 33 To determine the value of b, we can use the fundamental property of a straight line: the slope between any two points on the line is constant. The problem provides us with three points that all lie on the same line: (k, 13), (k + 7, […]<\/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-276166","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276166","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=276166"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276166\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=276166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=276166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=276166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}