Which table represents a linear function?
X
1
2
3
4
X
1
2
234
1
2
3
4
X12
A5951
y
y
-5
10
-15
20
SLE 888SK
10
20
40
-5<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine which table represents a linear function, we first need to understand the definition of a linear function. A linear function is one where the relationship between the independent variable (x) and the dependent variable (y) can be expressed in the form (y = mx + b), where (m) is the slope and (b) is the y-intercept. The key characteristic of a linear function is that it produces a straight line when graphed.<\/p>\n\n\n\n To analyze each table, we look for a constant rate of change between (x) and (y). This means that as (x) increases by a specific value, (y) should increase or decrease by a consistent amount.<\/p>\n\n\n\n In conclusion, Table 2<\/strong> represents a linear function because it has a constant rate of change. Each time (x) increases by 1, (y) consistently increases by 10, fitting the form (y = 10x). Tables with inconsistent changes between (x) and (y) do not exhibit linearity, while those with constant differences do. Understanding this relationship is essential in recognizing and graphing linear functions.<\/p>\n","protected":false},"excerpt":{"rendered":" Which table represents a linear function?X1234X122341234X12A5951yy-510-1520SLE 888SK102040-5 The Correct Answer and Explanation is : To determine which table represents a linear function, we first need to understand the definition of a linear function. A linear function is one where the relationship between the independent variable (x) and the dependent variable (y) can be expressed in […]<\/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-155928","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155928","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=155928"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155928\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155928"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155928"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155928"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
[
\\begin{array}{|c|c|}
\\hline
x & y \\
\\hline
1 & -5 \\
2 & 10 \\
3 & -15 \\
4 & 20 \\
\\hline
\\end{array}
]
The changes in (y) are inconsistent: from -5 to 10, (y) increases by 15, then from 10 to -15, (y) decreases by 25, and from -15 to 20, (y) increases by 35. Therefore, this does not represent a linear function.<\/li>\n\n\n\n
[
\\begin{array}{|c|c|}
\\hline
x & y \\
\\hline
1 & 10 \\
2 & 20 \\
3 & 30 \\
4 & 40 \\
\\hline
\\end{array}
]
Here, as (x) increases by 1, (y) increases by 10 consistently (10, 20, 30, 40). This constant change indicates a linear relationship.<\/li>\n<\/ol>\n\n\n\n