Question

(06.02 mc) the equation of line cd is y=3x-3. Write an equation of a line perpendicular to line cd in slope intercept form that contains points 3,1

Answer 1

y = -1/3x + 2

got it correct on my test

Answer 2

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 - 3 ← 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)`, hence

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

To find c substitute (3, 1) into the partial equation

1 = - 1 + c ⇒ c = 1 + 1 = 2

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