Answer
y=3x/2 - 1/2
Work Step by Step
Given points (4,-1) and (-2,3)
Their midpoint = ((4+(-2))/2, (-1+3)/2) = (1,1)
Find the slope of the line passing through the given points (m) :
$m=\frac{y_2-y_1}{x_2-x_1}=(-1-3)/(4-(-2))=-2/3$
Slope of a line perpendicular to this line = 3/2 (negative reciprocal)
Use the slope and point to find the line such that (x, y) is equidistant from the two points.
y = mx+b
1 = 3/2(1)+b
b = -1/2
y=3x/2 - 1/2
