Question

Find the equation of the line that is perpendicular to y=-2/3x and contain the point (4,-8)

Answer 1

y =
`(3)/(2)` x - 14

Explanation:

The equation of a line in slope- intercept form is

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

y = -
`(2)/(3)` x ← is in this form

with slope m = -
`(2)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(2)/(3) )` =
`(3)/(2)`, hence

y =
`(3)/(2)` x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 8) into the partial equation

- 8 = 6 + c ⇒ c = - 8 - 6 = - 14, so

y =
`(3)/(2)` x - 14 ← equation of perpendicular line

Answer 2

y = 3/2x - 14.

Explanation:

The slope of the perpendicular line is - 1 / -2/3

= 3/2.

Using the point slope form y-y1 = m(x-x1):

y - (-8) = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14.