What is the equation in standard form of a perpendicular line to y=3x+6 that passes through (5,-1)?

1 Answer
Feb 8, 2018

y=-1/3x+2/3

Explanation:

first, we need to identify the gradient of the line y=3x+6.
It is already written in the form y=mx+c, where m is the gradient.
the gradient is 3

for any line that is perpendicular, the gradient is -1/m
the gradient of the perpendicular line is -1/3

Using the formula y-y_1=m(x-x_1) we can work out the equation of the line.
substitute m with the gradient -1/3
substitute y_1 and x_1 with the coordinates given: (5,-1) in this case.
y--1=-1/3(x-5)
simplify to get the equation:
y+1=-1/3(x-5)
y=-1/3x+5/3-1

y=-1/3x+2/3