Question

The given line passes through the points (−4, −3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)?

y − 3 =
(x + 4)

Answer 1

Point-slope form is:

(y-y1)=m(x-x1)

So first find the slope from the two points given.

m=(y2-y1)/(x2-x1)

m=(1--3)/(4--4)

m=4/8

m=1/2

We want the line perpendicular to this one, so it will have a slope that is the negative reciprocal of this one, mathematically:

m1*m2=-1 in this case:

m/2=-1

m=-2

So we know the slope of the perpendicular line is -2 and we are given the point (-4,3) that we must pass through so:

y-3=-2(x+4)