Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 2 - Functions, Equations, and Graphs - 2-2 Direct Variation - Practice and Problem-Solving Exercises - Page 72: 30

Answer

$y$ does not vary directly with $x$.

Work Step by Step

To find the rule, we plug the $x$ values and $y$ values into the ratio $\frac{y}{x} = k$ to see if each set of $x$ and $y$ have the same constant of variation ($k$). If they do, then $y$ varies directly with $x$. $\dfrac{2}{1}\stackrel{?}= \dfrac{8}{3} \stackrel{?}= \dfrac{14}{5}$ Let's simplify each ratio: $2 \ne \frac{8}{3} \ne \frac{14}{5}$ In this exercise, $\frac{y}{x}$ is not constant, so $y$ does not vary directly with $x$.
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