Answer
y=-20x/3 -139/12
Work Step by Step
Given points (3,5/2) and (-7,1)
Their midpoint = ((3-7)/2, (5/2+1)/2) = (-2,7/4)
Find the slope of the line passing through the given points (m) :
$m=\frac{y_2-y_1}{x_2-x_1}=3/20$
Slope of a line perpendicular to this line = -20/3 (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
7/4 = -20/3(-2)+b
b = -139/12
y=-20x/3 -139/12
