Question

Write the equation of the line perpendicular to y = -3/4x that passes through the point (3,-8)

Answer 1

y =
`(4)/(3)` x - 12

Explanation:

The equation of a line in slope- intercept form is

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

y = -
`(3)/(4)` x ← is in slope- intercept form

with slope m = -
`(3)/(4)` , c = 0

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(4) )` =
`(4)/(3)` , then

y =
`(4)/(3)` x + c ← is the partial equation

To find c substitute (3, - 8) into the partial equation

- 8 = 4 + c ⇒ c = - 8 - 4 = - 12

y =
`(4)/(3)` x - 12 ← equation of perpendicular line