Answer
$ -x+3y=2$
Work Step by Step
We find the slope of the original line:
$m=\frac{-1-5}{5-3} = \frac{-6}{2}=-3$
The slope of the perpendicular line is the opposite reciprocal, which is 1/3. The line's midpoint is $(4,2)$, which is the average of the x and y endpoints. We obtain the equation, first using point slope form:
$y-2 = 1/3(x-4) \\ 3y-6=x-4 \\ -x+3y=2$
