How do you write the equation of the line that is perpendicular to the line #3x - 2y = 6# and passes through the point #(-1,2)#?

1 Answer
Douglas K.
Apr 29, 2017

When given a line of the standard form:
#ax+by=c#
Swap "a" and "b":
#bx+ay=c#
Then change the sign of "a" or "b":
#-bx+ay=c# or #bx-ay=c#
Find a new value for "c" by substituting in the given point.

Explanation:

Given:

#3x - 2y = 6#

Swap "a" and "b":

#-2x + 3y = 6#

We shall change the sign of -2:

#2x + 3y = 6#

Determine a new value for c by substituting in the point, #(-1,2)#:

#2(-1)+3(2) = 4#

The equation of the desired line is:

#2x + 3y = 4#

Here is a graph of the two lines and the point:Desmos.com

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