Answer:
y = x - 2
Step-by-step explanation:
Going from M to N, the run (increase in x) is 6, from 1 to 7. The rise (which is actually a decrease here) is -6, from 5 to -1. Thus, the slope of the line segment MN is m = rise / run = -6/6, or -1.
The slope of the perpendicular bisector is the negative reciprocal of this m = -1, and is +1.
This bisector passes through the midpoint of segment MN. The x-coordinate of this midpoint is (1 + 7)/2, or 4, and the y-coordinate is (5 - 1)/2, or 2: (4, 2).
Knowing both a point on this bisector (4, 2) and the slope of the bisector (+1), we can modify the point-slope form of the equation of a straight line, y - k = m(x - h), to obtain y -2 = 1(x - 4), or y = 2 + x - 4, or y = x - 2
