What is the equation of the line that goes through #(3,-4)# and is perpendicular to #y=3/2x-4#?

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Answer 1 · 2017-02-01T05:09:56

#y = -2/3x -2#

Because we can find the slope, and then solve for the constant by plugging in a point.

Perpendicular lines have opposite reciprocal slopes.

Above is a great explanation of why that is and some practice.

So the slope of this new line is #-2/3#. Lets start making a new equation in the form #y = mx + b#

#y = mx + b#

#y = -2/3x + b#

Now we plug in the given point #(3,-4)# to find what #b# should be

#-4 = -2*3/3 + b#

#b=-2#

So our final equation is:

#y = -2/3x -2#