Question

Determine whether the lines are parallel, perpendicular or neither: Line 1:4y−12=3x Line 2:2y−1.5x=−14

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We manipulate the expressions to model them in the pending-intersection form

Line 1:

$4y-12=3x\\4y=3x+12\\y=\frac{3}{4}x+\frac{12}{4}\\y=\frac{3}{4}x+3\\y=0.75x+3$

Line 2:

$2y - 1.5x = -14\\2y = 1.5x-14\\y = \frac {1.5} {2} x- \frac {14} {2}\\y = \frac {1.5} {2} x-7\\y = 0.75x-7$

By definition, we have that if two lines are parallel then their slopes are equal. It is observed that the slopes of both lines are equal, so the lines are parallel.

ANswer:

The lines are parallel