Question

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

Answer 1

Answer:

see explanation

Step-by-step 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 = $\frac{3}{4}$ x - 3 ← in slope- intercept form

with slope m = $\frac{3}{4}$

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

y = - $\frac{4}{3}$ x + 4 ← in slope- intercept form

with slope m = - $\frac{4}{3}$

Then

$\frac{3}{4}$ × - $\frac{4}{3}$ = - 1

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