Question

Are these lines parallel or perpendicular or neither y=1/4x+7 and y=4x-3

Answer 1

Remember, two lines are parallel if they have the same slope. They are perpendicular if you can multiply the two slopes together and get -1.
It looks like they already put the equations in y = mx + b form for you. In that case, the slope is m (the coefficient of x).

Answer 2

as slope of y=x/4+7 is 1/4=m1 and that of y=4x-3 is 4=m2
and m1 is not equal to m1 so they are not parallel
moreover m1*m2 is not equal to -1 so they are not perpendicular so they are niether