{"id":231259,"date":"2025-06-10T18:15:12","date_gmt":"2025-06-10T18:15:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=231259"},"modified":"2025-06-10T18:15:14","modified_gmt":"2025-06-10T18:15:14","slug":"the-function-y-3-75-1-5x-1-can-be-used-to-determine-the-cost-in-dollars-for-a-taxi-ride-of-x-miles","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/10\/the-function-y-3-75-1-5x-1-can-be-used-to-determine-the-cost-in-dollars-for-a-taxi-ride-of-x-miles\/","title":{"rendered":"The function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles"},"content":{"rendered":"\n
The function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles. what is the rate of change of the cost in dollars with respect to the number of miles?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Answer<\/strong><\/h3>\n\n\n\n
The rate of change of the cost in dollars with respect to the number of miles is $1.50 per mile<\/strong>.<\/p>\n\n\n\n
Explanation<\/strong><\/h3>\n\n\n\n
In mathematics, the “rate of change” of a linear function describes how one quantity changes in relation to another. For a function that models cost versus distance, the rate of change tells us how much the cost increases for every one-unit increase in distance. In the context of a linear equation, the rate of change is represented by the slope<\/strong> of the line.<\/p>\n\n\n\n
Here, y represents the total cost in dollars, and x represents the number of miles traveled. To determine the rate of change, we need to find the slope of this linear function. The most common form for a linear equation is the slope-intercept form, y = mx + b, where m is the slope (the rate of change) and b is the y-intercept.<\/p>\n\n\n\n
We can convert the given equation into this form through algebraic manipulation:<\/p>\n\n\n\n
\n
Start with the given function:<\/strong> y=3.75+1.5(x\u22121)y<\/em>=3.75+1.5(x<\/em>\u22121)<\/code><\/li>\n\n\n\n
Distribute the 1.5<\/strong>\u00a0across the terms inside the parentheses\u00a0(x – 1): y=3.75+1.5x\u22121.5(1)y<\/em>=3.75+1.5x<\/em>\u22121.5(1)<\/code> y=3.75+1.5x\u22121.5y<\/em>=3.75+1.5x<\/em>\u22121.5<\/code><\/li>\n\n\n\n
Combine the constant terms<\/strong>\u00a0(3.75 and -1.5) to simplify the equation: y=1.5x+(3.75\u22121.5)y<\/em>=1.5x<\/em>+(3.75\u22121.5)<\/code> y=1.5x+2.25y<\/em>=1.5x<\/em>+2.25<\/code><\/li>\n<\/ol>\n\n\n\n
Now the equation is in the standard slope-intercept form, y = mx + b. By comparing our equation to this form, we can clearly identify the slope, m.<\/p>\n\n\n\n
\n
m = 1.5<\/li>\n\n\n\n
b = 2.25<\/li>\n<\/ul>\n\n\n\n
The slope (m) is 1.5. Since y is in dollars and x is in miles, this slope represents a rate of $1.50 per mile. This means that for each additional mile the taxi travels, the total cost of the ride increases by $1.50. The value 3.75 in the original equation represents the cost of the first mile, and every subsequent mile adds $1.50 to the total fare.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
The function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles. what is the rate of change of the cost in dollars with respect to the number of miles? The Correct Answer and Explanation is: Answer The rate of change of the cost […]<\/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-231259","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231259","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=231259"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231259\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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