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 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:

`4y-12 = 3x`

We manipulate the equation to convert it into the slope-intersection form
`y = mx + b`

Where:

m: It's the slope

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

So:

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

From the second equation given we have:

`2y-1.5x = -14`

We manipulate:

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

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

ANswer:

The lines are parallel.