Answer
$-3$
Work Step by Step
For two lines to be perpendicular, their slopes must be opposite reciprocals, so we are looking for the opposite reciprocal of the slope of the given equation. In order to find the slope of the given equation, we must first put it into slope-intercept form. To do so, we add $y-2$ to both sides of the equation, giving us $y=\frac{1}{3}x-2$
Since the $\frac{1}{3}$ is the coefficient of $x$ in this equation, the slope is $\frac{1}{3}$. The opposite reciprocal of $\frac{1}{3}$ is $-3$.
