Lines are perpendicular to each other when their slopes are of the opposite parity (plus or minus) and the reciprocal of each other. I will check the answer that you have given. Already, in one of the equations, (y - 3 = 4/7x)we can see the slope. Now we just need to find the slope in 7x+4y=20. We can do this by isolating y and then getting y by itself. Doing this, we get:
4y = -7x + 20
y = -7/4x + 5
Since we can see that the slopes of the two lines multiply to negative one, then you are right, the two lines are parallel.