What is the equation of the line that is perpendicular to y=1/5x+4 and that passes through (5,—4)?

Work Shown:

The given equation y = (1/5)x+4 is in the form y = mx+b with m = 1/5 as the slope.

Apply the negative reciprocal to this slope to go from 1/5 to -5/1 or -5.

The original slope is 1/5 and the perpendicular slope is -5. Note the two slopes multiply to -1. This applies to any pair of perpendicular lines as long as neither line is vertical.

We'll use m = -5 as the slope and (x,y) = (5,-4) to find the y intercept

y = mx+b

-4 = -5*5+b

-4 = -25+b

-4+25 = b

21 = b

b = 21

The y intercept of the perpendicular line is b = 21

With m = -5 and b = 21, we go from y = mx+b to y = -5x+21 which is the equation of the perpendicular line.