Question

Write the equation of the line that passes through the point (6, -2) and is perpendicular to the line

y = 1/3x+8.

Answer 1

y = - 3x + 16

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =
`(1)/(3)` x + 8 ← is in slope- intercept form

with slope m =
`(1)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(3) )` = - 3, so

y = - 3x + c ← is the partial equation of the perpendicular line

To find c substitute (6, - 2) into the partial equation

- 2 = - 18 + c ⇒ c = - 2 + 18 = 16

y = - 3x + 16 ← equation of perpendicular line