Question

Write the equation of the line passing through (6,-2) that is perpendicular to y=3x-19

Answer 1

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

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 - 19 ← 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 (6, - 2 ) into the partial equation

- 2 = - 2 + c ⇒ c = - 2 + 2 = 0

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