Question

What is the equation of the

line that is perpendicular to y = -3x + 6 and
passes through the point (3, 5)?

Answer 1

y =
`(1)/(3)` x + 4

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 + 6 ← 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)` , then

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

to find c substitute (3, 5 ) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y =
`(1)/(3)` x + 4 ← equation of perpendicular line