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 71: 9

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 $x$: $\dfrac{22}{11} = \dfrac{32}{16} \ne \dfrac{42}{7}$ The first two ratios can be simplified to $2$, but the last ratio simplifies to $6$; therefore, in this exercise, $\dfrac{y}{x}$ is not constant, and $y$ does not vary directly with $x$.
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