Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 83

Answer

Doubling $x$ will cause the value of $y$ to double because in a direct variation, the change applied to one variable will result to the same change in the other variable.

Work Step by Step

RECALL: When $y$ varies directly as $x$, the equation of the variation is $y=kx$ . Doubling $x$ means $2x$ so replacing $x$ with $2x$ gives: $y=k(2x) \\y=2kx$ Notice that $2kx$ is twice of $kx$ Thus, doubling $x$ causes $y$ to double its value. This is because in a direct variation, whatever change is made to the value of $x$ will result to the same direct change in the value of $y$.
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