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 = [tex]\frac{3}{4}[/tex] x - 3 ← in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
3y = 12 - 4x = - 4x + 12 ( divide terms by 3 )
y = - [tex]\frac{4}{3}[/tex] x + 4 ← in slope- intercept form
with slope m = - [tex]\frac{4}{3}[/tex]
Then
[tex]\frac{3}{4}[/tex] × - [tex]\frac{4}{3}[/tex] = - 1
Since the product of their slopes = - 1 then the lines are perpendicular
