Answer
y=-5x/13 -2/13
Work Step by Step
Given points (6,5) and (1,-8)
Their midpoint = ((6+1)/2, (5-8)/2) = (7/2,-3/2)
Find the slope of line passing through the given points (m) :
$m=\frac{y_2-y_1}{x_2-x_1}=13/5$
Slope of a line perpendicular to this line = -5/13 (negative reciprocal).
Use the slope and a point to find the line such that (x, y) is equidistant from the two points.
y = mx+b
-3/2 = -5/13(7/2)+b
b = -2/13
y=-5x/13 -2/13
