What is the equation of a line that is perpendicular to $2x-3y=4$ and has a $y$-intercept of $-5$?

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Start by finding the slope of the line given. We can do this by changing the equation from standard form into slope-intercept form.

$$2x-3y=4$$ $$2x-4=3y$$ $$\frac{2}{3}x-\frac{4}{3}=y$$ $$m=\frac{2}{3}$$

We find the slope that is perpendicular by taking the opposite reciprocal.

$$\perp m=-\frac{1}{m}$$ $$\perp m=-\frac{3}{2}$$

Only one answer choice has the correct slope.