How do you find an equation of a line containing the point (-2, 2), and perpendicular to the line 2(y + 1) = x?

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Answer 1 · 2017-09-06T08:25:33

See explanation.

First we have to transform the given equation to form #y=ax+b# :

#2(y+1)=x#

#2y+2=x#

#2y=x-2#

#y=1/2x-1#

Now we can write the equation of a line perpendicular to the given one.

Two lines are perpendicular if and only if product of their slopes is #-1#:

#1/2*m=-1#

#m=-2#

So the line we are looking for has equation:

#y=-2x+b#

Now we have to calculate the value of #b# for which point #(-2;2)# belongs to the line:

To do this we have to put the point's coordinates as #x# and #y#:

#2=-2*(-2)+b#

#2=4+b#

#b=-2#

Finally the line perpendicular to #2(y + 1) = x# passing rhrough #(-2,2)# is

#y=-2x-2#