#### Answer

$y=\frac{1}{3}|x|$.

#### Work Step by Step

The absolute value functions have the form $y=a|x-b|+c$ where $(b,c)$ is the vertex of the function.
Hence here because the vertex is at $(0,0)$, $y=a|x|$.
Since $(-3,1)$ is on the function, plugging in the values we get: $1=a|-3||\\1=3a\\a=\frac{1}{3}$.
Thus $y=\frac{1}{3}|x|$.