why was the value of y for the function y = 5x + 1 always be greater than that for the function y=4x+2 when x>1

Lets compare both equations so we can explain the reason for it, and see it clearly:

y1 = 5x + 1

y2 = 4x + 2

y1 > y2

5x + 1 > 4x + 2

To see why that happens we need to solve for x:

5x - 4x > 2 - 1

x > 1

Therefore, the first equation is greater than the second for values of x > 1