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.