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

1 Answer
Mar 19, 2016

Answer:

#y = -2x - 7#

Explanation:

First, get the slope #m'# of the line that the line in question is perpendicular to.

#m' = (y_1 - y_2) / (x_1 - x_2)#

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

#=> m' = -1/-2 = 1/2#

Next, to get the slope #m# of the desired line, we get the negative reciprocal of the slope #m'# of the line is the perpendicular with

#m = -1/(m')#

#=> m = -1/(1/2) = -2#

Now that we have the slope #m# of the desired line, we must get the #y#-intercept of the line. We do this by substituting the coordinates of the point where we know the line passes through

#y = mx + b#
#=> y = -2x + b#

#=> 1 = -2(-4) + b#

#=> 1 = 8 + b#
#=> b = -7#

Hence, the equation of the line is

#y = -2x - 7#