Question

Find the equation of the line perpendicular to y= -2x+1 that also intersects the point (8, 2)

Answer 1

The slope of the perpendicular is the negative reciprocal of the original line, so m = -1/(-2) = 1/2.

The general line of slope m through (a,b) is

$y - b = m(x-a)$

So the line we seek is

$y - 2 = \frac 1 2 ( x - 8)$

$y = \frac 1 2 x - 2$

Answer: y = 1/2  x + -2