The line through `(-3,9)` and `(4,4)` has slope `m_1=(4-9)/(4-(-3))=(-5)/7`

The line through `(9,-1)` and `(4,-8)` has slope `m_2=(-8-(-1))/(4-9)=(-7)/(-5)=7/5`

Now

`m_1m_2=(-5)/7xx7/5=-1`

Since the product of the slopes is `−1`, we conclude the lines are perpendicular.

Note: We could have sketched the lines to determine whether they were parallel or perpendicular.