Question

Find the equation of the line described.

Perpendicular to y = 3x + 6; passing through the point (4,5).
The line equation is y =

Answer 1

y = -
`(1)/(3)` x +
`(19)/(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 + 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)` , thus

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

To find c , substitute (4, 5) into the partial equation

5 = -
`(4)/(3)` + c ⇒ c = 5 +
`(4)/(3)` =
`(19)/(3)`

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