Answer
The constant of variation is $\frac{2}{3}$, and $y$ varies directly with $x$.
The function rule is $y = \frac{2}{3}x$.
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 $x$.
$\frac{6}{9}$ ? $\frac{8}{12}$ ? $\frac{10}{15}$ = ?
Let's simplify each ratio:
$\frac{2}{3}$ = $\frac{2}{3}$ = $\frac{2}{3}$
Each ratio can be simplified to $\frac{2}{3}$; therefore, the constant of variation is $\frac{2}{3}$, and $y$ varies directly with $x$.
The function rule is $y = \frac{2}{3}x$.