What is the equation of a line that is perpendicular to - x + 2y = 4 and passes through the point (-2,1)?

A. y = -2x - 3

B. y = 2x + 4

C. y = x + 2

D. y = 2x - 4

1 Answer
Geoff K.
Nov 21, 2016

A. #y=-2x-3#.

Explanation:

First, rewrite the equation in slope-intercept form: #y=mx+b#.

#-x+2y=4#
#=>2y=x+4#
#=>y=1/2x+2#

So the slope of the given line is #m=1/2#.

Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope #m#, then a line perpendicular to this has slope #m^"*"=(-1)/m#. That means the slope of our perpendicular line is

#m^"*"=(-1)/(1//2)=-2#.

Knowing the new slope and a point, we can find an equation for our perpendicular line by using the slope-point equation #y-y_1=m(x-x_1)#, or by plugging in the given #(x,y)# point (and the new slope #m^"*"#) into #y=mx+b# to find #b# for the new line.

#y-y_1=m(x-x_1)#
#=>y-1=-2[x-(-2)]#
#=>y-1=-2[x+2]#
#=>y=-2x-3#

or

#y=mx+b#
#=>1=-2(-2)+b#
#=>1=4+b#
#=>b=-3#

#:.y=mx+b# becomes #y=-2x-3#.

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