Question

Find the equation for the line that passes through the point (1,-5) and that is perpendicular to the line with the equation y=1/3x-2/3

Answer 1

y = - 3x - 2

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 -
`(2)/(3)` ← 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 , then

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

To find c substitute (1, - 5 ) into the partial equation

- 5 = - 3 + c ⇒ c = - 5 + 3 = - 2

y = - 3x - 2 ← equation of perpendicular line