Which pair of lines are perpendicular to one another ?

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. 

Yes she is correct. when you do 1/5 the tbe is their to represent the fraction. so yes, kathy got it