Question

Which equation is perpendicular to 3x - y = 9 and goes through the point (6,6)

Answer 1

y = -
`(1)/(3)` x + 8

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 3x - y = 9 into this form by subtracting 3x from both sides

- y = - 3x + 9 ( divide all terms by - 1 )

y = 3x - 9 ← 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)`, thus

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

To find c substitute (6, 6) into the partial equation

6 = - 2 + c ⇒ c = 6 + 2 = 8

y = -
`(1)/(3)` x + 8 ← equation of perpendicular line