Which of these is equivalent to the equation below?
y=mx+b
A. b=y\u2212mx
B. x=y\u2212b\/m
\u200bC. b=mx\/y
D. x=y\/mb<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine which option is equivalent to the equation (y = mx + b), we need to manipulate the original equation and analyze each option.<\/p>\n\n\n\n The equation (y = mx + b) represents a linear equation in slope-intercept form, where (m) is the slope of the line, (b) is the y-intercept, and (x) and (y) are the variables. To find an equivalent expression, we can solve for (b), (x), or (y).<\/p>\n\n\n\n Rearranging the equation:<\/strong><\/p>\n\n\n\n Now, let\u2019s examine the other options to see if they represent equivalent forms or not.<\/p>\n\n\n\n Conclusion:<\/strong> Which of these is equivalent to the equation below?y=mx+bA. b=y\u2212mxB. x=y\u2212b\/m\u200bC. b=mx\/yD. x=y\/mb The Correct Answer and Explanation is: To determine which option is equivalent to the equation (y = mx + b), we need to manipulate the original equation and analyze each option. The equation (y = mx + b) represents a linear equation […]<\/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-160572","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160572","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=160572"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160572\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
[
b = y – mx
]
This directly corresponds to option A<\/strong>: (b = y – mx).<\/li>\n<\/ol>\n\n\n\n\n
[
x = \\frac{y – b}{m}
]
Rearranging (y = mx + b) gives us (y – b = mx), leading to (x = \\frac{y – b}{m}). While this rearrangement is valid, it is not the same as the original equation; instead, it offers a way to find (x).<\/li>\n\n\n\n
[
b = \\frac{mx}{y}
]
This is incorrect because it doesn’t follow from the original equation. Instead, it falsely suggests a direct relationship between (b), (m), (x), and (y).<\/li>\n\n\n\n
[
x = \\frac{y}{mb}
]
This option is also incorrect and not derived from the original equation. It misrepresents the relationship between (x), (y), (m), and (b).<\/li>\n<\/ol>\n\n\n\n
The only correct option that is directly derived from the equation (y = mx + b) is A. (b = y – mx)<\/strong>. This option correctly isolates (b), confirming its equivalence to the original equation while maintaining the relationships of the variables involved. Thus, option A is the only valid choice here.<\/p>\n","protected":false},"excerpt":{"rendered":"