Question

Create the equation of a line that perpendicular to 2y=14+2/3x and passes through the point (-2,8).

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 )

Rearrange 2y = 14 +
`(2)/(3)` x into this form

Divide all terms by 2

y = 7 +
`(1)/(3)` x ← 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, hence

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

To find c substitute (- 2, 8) into the partial equation

8 = 6 + c ⇒ c = 8 - 6 = 2

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