How do you find the equation of the line in slope-intercept form that is perpendicular to the line -4x - 3y = 9 and passes through (12, -7)?

1 Answer
Aug 26, 2015

Answer:

#y=3/4x-16#

Explanation:

#-4x-3y=9#
can be re-written in slope intercept form as:
#y = -4/3x-3#
and therefore has a slope of #(-4/3)#

Lines which are perpendicular to each other have slopes that are the negative reciprocal of one another.

Therefore any line perpendicular to #-4x-3y=9# has a slope of
#m= 3/4#

Since the desired line has a slope of #3/4# and passes through #(12,-7)# we can write it's equation in slope-point form as:
#(y-(-7)) = 3/4(x-12)#

Simplifying:
#y+7 = 3/4x-9#
or
#y=3/4x-16color(white)("XXXX")#which is slope-intercept form.