40Perpendicular bisector

Find the equation of the perpendicular bisector of the segment from (0, 0) to (8, 4), in the form y = mx + b.

The perpendicular bisector is y = −2x + 10. The midpoint of (0,0) and (8,4) is (4,2), the segment's slope is 1/2, so the perpendicular slope is −2; plugging into point-slope form and simplifying gives y = −2x + 10, and at x = 4 it correctly gives y = 2.