Answer
$x = -3$
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:
$4 = k(-2)$
Divide both sides by $-2$ to isolate $k$:
$k = -2$
Our constant of variation is $-2$.
Now, we want to find $x$ when $y$ is a specific value. We plug $y$ and the $k$ we just found into the formula for direct variation:
$6 = -2x$
Divide both sides by $-2$:
$x = -3$
