Answer
$y = −\frac{7}{2}$
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:
$−2 = k(4)$
Divide both sides by $4$ to isolate $k$:
$k = −\frac{1}{2}$
Our constant of variation is $−\frac{1}{2}$.
Now, we want to find $y$ when $x$ is a specific value. We plug $x$ and the $k$ we just found into the formula for direct variation:
$y = −\frac{1}{2}(7)$
Multiply to simplify:
$y = −\frac{7}{2}$
