Chapter 2 Linear Equations and Functions - 2.7 Use Absolute Value Functions and Transformations - 2.7 Exercises - Skill Practice - Page 127: 17

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

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