For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
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:
[tex]4y-12=3x\\4y=3x+12\\y=\frac{3}{4}x+\frac{12}{4}\\y=\frac{3}{4}x+3\\y=0.75x+3[/tex]
Line 2:
[tex]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[/tex]
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
