What is the equation of a line that is perpendicular to the graph shown below and has an $x\text{-intercept}$ of $(3,0)$?

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We begin by finding the slope of the line shown. We can do this choosing two points and calculating rise over run graphically. Using the points $(-2,-1)$ and $(-1,2)$, we can count the rise to be 3 and the run to be 1, giving a slope of 3. The slope of an equation perpendicular to this would be $-\frac{1}{3}$. Only one answer choice has the correct slope.

Attempting to sketch the line perpendicular to the one on the graph and passing through the point $(3,0)$ would give us something like the following:

The sketched line has a $y$-intercept around $y=1$ and a negative slope. Only one answer choice matches these descriptions.