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:
[tex]4y-12 = 3x[/tex]
We manipulate the equation to convert it into the slope-intersection form [tex]y = mx + b[/tex]
Where:
m: It's the slope
y: It is the cut-off point with the y axis.
So:
[tex]4y = 3x + 12\\y = \frac {3} {4} x + \frac {12} {4}\\y = 0.75x + 3[/tex]
From the second equation given we have:
[tex]2y-1.5x = -14[/tex]
We manipulate:
[tex]2y = 1.5x-14\\y = \frac {1.5} {2} x- \frac {14} {2}\\y = 0.75x-7[/tex]
It is observed that the slopes are equal, so the lines are parallel,
ANswer:
The lines are parallel.
