Question

Find the equation of the line through the point (–2, –2) that is perpendicular to the line y = 2x – 1.

A.
y = –2x – 9/4
B.
y = 2x – 3
C.
y = –1/2x – 3
D.
y = –1/2x + 3

Answer 1

For lines to be perpendicular to each other their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

Since y=2x-1 has a slope of 2, our perpendicular line must have a slope of:

2m=-1, m=-1/2, so our perpendicular line will be of the form:

y=-x/2+b, using the point (-2,-2) we can solve for the y-intercept, or "b".

-2=--2/2+b

-2=1+b

b=-3, then our perpendicular line is:

y=-x/2-3 or more neatly

y=-0.5x-3