Line l passes through (1,-3) and i perpendicular to #y=1/5x-7# What the equation of line l?

1 Answer
Apr 28, 2018

Answer:

The slope of the perpendicular is the negative reciprocal of the slope of the given line, and the constant is determined by the point it passes through, giving #y =-5x+2. #

Explanation:

The usual method is to say the slope is #1/5# so the slope of the perpendicular is the negative reciprocal #-5# so #y=-5x + b# means #-3 = -5(1) + b# or #b=2# so #y =-5x+2#.

My preferred method is to bring #x# and #y# to the same side, #y - 1/5 x = -7# then swap the coefficients on #x# and #y#, negating one of them, and set the constant to fit: #1/5 y +x = (1/5) (-3) + 1 = 2/5# or multiplying through, #y + 5x = 2.#