Question

What is an equation for the line perpendicular to y = 3x - 1 that passes through (-9, -2)?

Answer 1

y = -1/3x - 5

Explanation:

Perpendicular lines have negative reciprocal slopes, so the line is:

y = -1/3x + b

Finding the value of b, using the given point (-9, -2)

-2 = -1/3*(-9) + b

-2 = 3 + b

b = -2 - 3

b = -5

The line is

y = -1/3x - 5

Hopefully, this helps!

Answer 2

y = -
`(1)/(3)`x - 5

Explanation:

A perpendicular line will have a slope that is a negative reciprocal slopes to the slope of the original line, so far our equation looks like this:

y = -
`(1)/(3)`x + b

To find our b (y-axis intercept) we will plug in the point they gave us and solve

y = -
`(1)/(3)`x + b

(plug in) -2 = -
`(1)/(3)`(-9) + b

(mutiply) -2 = 3 + b

(subtract three from both sides)

-5 = b

(flip) b = -5

(plug in) y = -
`(1)/(3)`x - 5