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: 7

Answer

$y$ varies directly with $x$. The constant of variation is $7$. The function rule is $y = 7x$.

Work Step by Step

To find the rule, we plug the $x$ values and $y$ values into the ratio $\dfrac{y}{x} = k$ to see if each set of $x$ and $y$ have the same constant of variation ($k$). If they do, then $y$ varies directly with $x$: $\dfrac{14}{2} = \dfrac{21}{3} = \dfrac{35}{5} = 7$ Each ratio can be simplified to $7$; therefore, the constant of variation is $7$, and $y$ varies directly with $x$. The function rule is $y = 7x$.
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