Question

Write an equation for a line perpendicular to y=3x+2 and passing through the point (-9,6)

y=

Answer 1

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

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 + 2 ← 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 (- 9, 6 ) into the partial equation

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

3 = c

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