Question

Which equation represents a line that is perpendicular to line PQ?

A. y = 3x - 2
B. y = 1/3x + 4
C. y = -1/3x - 5
D. y = -3x + 6

Answer 1

B. y=1/3x+4

Explanation:

Hi there!

We are given the line PQ and we want to find the line that is perpendicular to it

Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So first, let's find the slope of the line PQ

The point P is given as (-8, 7) and the point Q is given as (-4, -5)

The formula for the slope calculated from two points is
`(y_2-y_1)/(x_2-x_1)` where (
`x_(1)`
`y_1`) and (
`x_2`,
`y_2`) are points

We have the needed information for the slope, but let's label the values of the points to avoid any confusion

x1=-8

y1=7

x2=-4

y2=-5

Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):

m=
`((-5-7))/((-4--8))`

simplify

m=
`(-5-7)/(-4+8)`

add

m=-12/4

divide

m=-3

So the slope of the line PQ is -3

As said above, perpendicular lines have slopes that have a product of -1

So to find the slope of the line perpendicular to PQ, use this formula:

-3m=-1

divide both sides by -3

m=1/3

The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.

Hope this helps!