Answer
The slope of the line given is $m=-\dfrac{1}{3}$ and its $y$-intercept is $(0,0)$
Work Step by Step
$g(x)=-\dfrac{1}{3}x$
Substitute $g(x)$ by $y$, for representative purposes:
$y=-\dfrac{1}{3}x$
The equation of this line is now in slope-intercept form. This form is $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept.
In this case, $m=-\dfrac{1}{3}$ and $b=0$
The slope of the line given is $m=-\dfrac{1}{3}$ and its $y$-intercept is $(0,0)$
The graph is shown below: