Answer
y=-16x/21 -13/56
Work Step by Step
Given points (-1/2,-4) and (7/2,5/4)
Their midpoint = ((-1/2+7/2)/2, (-4+5/4)/2) = (3/2,-11/8)
Find the slope of the line passing through the given points (m) :
$m=\frac{y_2-y_1}{x_2-x_1}=21/16$
Slope of a line perpendicular to this line = -16/21 (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
-11/8 = -16/21(3/2)+b
b = -13/56
y=-16x/21 -13/56
