Question

which line is perpendicular to a line that has a slope of $-\frac{3}{5}$?○ line jk○ line lm○ line no○ line pq

Explanation:

Answer:

First, calculate the slope of each line:

• Line JK: slope = $\frac{3}{2}$
• Line LM: slope = $2$
• Line NO: slope = $-\frac{3}{2}$
• Line PQ: slope = $-\frac{2}{3}$

The slope perpendicular to $-\frac{3}{2}$ is $\frac{2}{3}$? No, correction: perpendicular slope to $m$ is $-\frac{1}{m}$, so to $-\frac{3}{2}$ it is $\frac{2}{3}$? Wait no, $-\frac{1}{-\frac{3}{2}} = \frac{2}{3}$. Wait no, line LM has slope 2? No, let's recheck: Line LM goes from (-3,-4) to (2,6): slope $\frac{6 - (-4)}{2 - (-3)} = \frac{10}{5} = 2$. Line JK: from (-4,-5) to (0,-1): slope $\frac{-1 - (-5)}{0 - (-4)} = \frac{4}{4} = 1$? No, wait the correct perpendicular slope to $-\frac{3}{2}$ is $\frac{2}{3}$. Wait line PQ: from (-5,-3) to (1,1): slope $\frac{1 - (-3)}{1 - (-5)} = \frac{4}{6} = \frac{2}{3}$. Oh right! So:
Line PQ.

Wait no, the question says perpendicular to slope $-\frac{3}{2}$. The perpendicular slope is $\frac{2}{3}$, which is line PQ.