Question

Prove that lines 3x-4y=12 and 3y=12-4x are perpendicular.

Answer 1

see explanation

Explanation:

If 2 lines are perpendicular then the product of their slopes equals - 1

The equation of a line in slope- intercept form is

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

Consider the given equations

3x - 4y = 12 ( subtract 3x from both sides )

- 4y = - 3x + 12 ( divide terms by - 4 )

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

with slope m =
`(3)/(4)`

3y = 12 - 4x = - 4x + 12 ( divide terms by 3 )

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

with slope m = -
`(4)/(3)`

Then

`(3)/(4)` × -
`(4)/(3)` = - 1

Since the product of their slopes = - 1 then the lines are perpendicular