What is the equation of the line that passes through #(-2,1) # and is perpendicular to the line that passes through the following points: #(1,4),(-2,3) #?

1 Answer
David G.
Mar 30, 2016

First step is to find the slope of the line through #(1,4)# and #(-2,3)#, which is #1/3#. Then all lines perpendicular to this line have slope #-3#. Finding the y-intercept tells us the equation of the line we are looking for is #y=-3x-5#.

Explanation:

Slope of the line through #(1,4)# and #(-2,3)# is given by:

#m=(y_2-y_1)/(x_2-x_1)=(3-4)/((-2)-1)=(-1)/(-3)=1/3#

If the slope of a line is #m#, lines perpendicular to it have slope #-1/m#. In this case, the slope of the perpendicular lines will be #-3#.

The form of a line is #y=mx+c# where #c# is the y-intercept, so if we substitute in #-3# as the slope and the given points #(-2,1)# for #x# and #y#, we can solve to find the value of #c#:

#1=-3(-2)+c#

#c=-5#

So the equation of the line we want is #y=-3x-5#

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