How do you write an equation of a line perpendicular to y= 3/4x - 2 and passes through (-12,7)?

1 Answer
Nov 1, 2015

Answer:

#y = -4/3x -9#

Explanation:

First we need to get the slope of the perpendicular line

The slope of a perpendicular line is equal to the negative inverse of the slope of the given line

#y = mx + b#

#y = 3/4x - 2#

#=> m = 3/4#

#m' = -1/m#

#=> m' = -1 / (3/4)#

#=> m' = -4/3#

Now that we have the slope, we need to find the y-intercept.
To find the y-intercept, we need to plug-in values of #x# and #y# that the line passes through

#y' = m'x' + b#

#=> y' = -4/3x' + b#

#=> 7 = -4/3(-12) + b#

#=> 7 = 16 + b#

#=> b = -9#

Therefore, the equation of the line is

#y = -4/3x -9#