Question

What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (-6, 9)?

y=-1/3x+3
y=-1/3x+7
y=3x-33
y = 3x + 27

Answer 1

y = -
`(1)/(3)` x + 7

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)` , then

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

to find c substitute (- 6, 9 ) into the partial equation

9 = -
`(1)/(3)` (-6) + c = 2 + c ( subtract 2 from both sides )

7 = c

y = -
`(1)/(3)` x + 7 ← equation of perpendicular line