Part A
In order to verify if these two lines are parallel, let's rewrite the given equations:
3x - 4y = -2
-4y = -2 - 3x
4y = 2 + 3x
4y = 3x + 2
y = (3/4)x + 2/4
y = 0.75x + 0.5
and
4y = 3x - 12
y = (3/4)x - 12/4
y = 0.75x - 3
As we can see, the slope of both lines is 0.75. So, since they have the same slope, they are parallel lines.
Part B
Now, let's remember that two lines are perpendicular when the slope m2 of one line equals the negative reciprocal of the slope m1 of the other line:
m2 = -1/m1
Now, let's rewrite the given equations, and then compare their slopes:
8x - 2y = 7
-2y = 7 - 8x
2y = 8x - 7
y = (8/2)x - 7/2
y = 4x - 3.5
and
3x + 12y = 9
12y = 9 - 3x
12y = -3x + 9
y = (-3/12)x + 9/12
y = (-1/4)x + 0.75
As we can see, the slope of these lines are:
m1 = 4
m2 = -1/4
Comparing them, we find that:
m2 = -1/4 = -1/m1
m2 = -1/m1
Therefore, these lines are perpendicular.