First, make the given equation turn into y=mx+b format.
4x-y=6
4x-6=y
So, now we know the line we have to figure out which is parallel to, now since we know that parallel lines have to keep the same slope and the only thing that changes is the b part of it.
x-4y=-12
x+12=4y
1/4x+3=y
The first answer is NOT parallel
y-2=-4(x+1)
y-2=-4x-4
y=-4x-2
The second answer is NOT parallel
y+1=4(x-2)
y+1=4x-8
y=4x-9
The third answer IS parallel
y=4x+11
The fourth answer IS parallel
y=-12-3
y=-15
This would be a vertical or horizontal line it cannot be parallel to something with a slope
8x-2y=6
8x-6=2y
4x-3=y
The sixth answer IS parallel
