Question

which of the following equations represent a line that is perpendicular to y=-3x+6 and passes through the point (3,2)

Answer 1

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

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

to find c substitute (3, 2 ) into the partial equation

2 = 1 + c ⇒ c = 2 - 1 = 1

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