#### Answer

$10x - 8y = -39$

#### Work Step by Step

We find the slope of the original line:
$m=\frac{5-1}{-4-1} = \frac{-4}{5}$
The slope of the perpendicular line is the opposite reciprocal, which is 5/4. The line's midpoint is $(-1.5,3)$, which is the average of the x and y endpoints. We obtain the equation, first using point slope form:
$y-3 = 5/4(x+1.5) \\ 4y-12=5(x+1.5) \\ 4y-12 = 5x + 7.5 \\ -5x+4y=19.5 \\ 10x - 8y = -39$