Answer
$y = 21$
Work Step by Step
First, we need to find the constant of variation for this exercise. We have an $x$ value and a $y$ value. Let's plug these values into the formula for direct variation, $y = kx$ to find $k$, the constant of variation:
$-7 = k(-3)$
Divide both sides by $-3$ to isolate $k$:
$k = \frac{7}{3}$
Our constant of variation is $\frac{7}{3}$.
Now, we want to find $y$ when $x$ is a specific value. We plug $y$ and the $k$ we just found into the formula for direct variation:
$y = \frac{7}{3}(9)$
Multiply to simplify:
$y = \frac{63}{3}$
Simplify the fraction:
$y = 21$