Question

What is the equation of the line that is perpendicular to the

given line and has an x-intercept of 6?
y=-3x+8
-10-8-64-222
6
8
10
x
(4-2)

Answer 1

y =
`(1)/(3)` x - 2

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 8 ← is in slope- intercept form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-3)` =
`(1)/(3)`, thus

y =
`(1)/(3)` x + c ← is the partial equation

To find c substitute the coordinates of the x- intercept (6, 0) into the partial equation

0 = 2 + c ⇒ c = 0 - 2 = - 2

y =
`(1)/(3)` x - 2 ← equation of perpendicular line