Answer
$G$
Work Step by Step
For two lines to be perpendicular to one another, the slopes of the two lines must be negative reciprocals of one another; therefore, we must find the slope of the given line first.
The slope of a line is given by the formula:
$m = \dfrac{y_2 - y_1}{x_2 - x_1}$
Looking at the graph of the line, we see that one point on the graph is the origin $(0, 0)$, and another point is $(1, -3)$. Let us plug these points into the formula to figure out the slope:
$m = \dfrac{-3 - 0}{1 - 0}$
Let us simplify by subtracting:
$m = \dfrac{-3}{1}$
Simplify the fraction:
$m = -3$
The negative reciprocal of $-3$ is $\dfrac{1}{3}$.
All of the choices are in slope-intercept form, so we just look for the slope that is $\dfrac{1}{3}$.
Option F is incorrect. Its slope is $-3$.
Option H is incorrect. Its slope is $-\frac{1}{3}$.
Option I is incorrect. Its slope is $3$.
Option G is correct. Its slope is $\dfrac{1}{3}$.
Therefore, the answer is option $G$.
