Answer
The slopes are opposite reciprocals, so the lines are perpendicular.
Work Step by Step
$y-4=3(x+2) \rightarrow y=3x+10$
Find the slope of each line by writing its equation in slope-intercept form:
$2x+6y=10$
$6y=-2x+10$
$y=\frac{-1}{3}x+\frac{5}{3}$
The slope of the graph of $y=\frac{-1}{3}x+\frac{5}{3}$ is $\frac{-1}{3}$
The slope of the graph of $y=3x+10$ is $3$
The slopes are not the same, so the lines cannot be parallel. Multiply the slopes to see if they are opposite reciprocals.
$\frac{-1}{3} \times 3=-1$
The slopes are opposite reciprocals, so the lines are perpendicular.
