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

1 Answer
Taniya
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#

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