Question

find the slope of a line perpendicular to the line whose equation is 4x - 6y = -24. fully simplify your answer.

Explanation:

Step1: Rewrite original line in slope-intercept form

Original equation: $4x - 6y = -24$. Subtract $4x$: $-6y = -4x -24$. Divide by $-6$: $y = \frac{2}{3}x + 4$. Slope of original line is $\frac{2}{3}$.

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal: $-\frac{3}{2}$.

Answer:

$-\frac{3}{2}$