Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.7 - Variation and Problem Solving - Exercise Set - Page 397: 8


$k=.16$, $y=.16x$

Work Step by Step

If y varies directly as x, we know that the variables x and y can be related by the function $y=kx$, where k is the constant of proportionality. If $y=.4$ when $x=2.5$, then we know that $.4=2.5k$ (or $\frac{2}{5}=\frac{5}{2}k$). Multiply both sides by $\frac{2}{5}$. $k=\frac{2}{5}\times\frac{2}{5}=\frac{2\times2}{5\times5}=\frac{4}{25}=.16$ Therefore, the constant of variation is $k=.16$ and the direct variation equation is $y=.16x$.
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