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

For this case we have to by definition:

If two lines are parallel then their slopes are equal.

If two lines are perpendicular then the product of their slopes is equal to -1.

We have the following equations:

We manipulate the equation to convert it into the slope-intersection form

Where:

m: It's the slope

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

So:

From the second equation given we have:

We manipulate:

It is observed that the slopes are equal, so the lines are parallel,

The lines are parallel.

take it another