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

Multiplication scales faster than addition. You're not just adding the last number, you're adding an additional count of the first number. 

5 x 5 is a shortcut to writing 5 + 5 + 5 + 5 + 5 

So, if x is 1:
5(1)+1 = 5 (times nothing really) + 1 = 6
4(1)+2 = 4 (times nothing again) + 2 = 6

If x is 2:
5(2)+1 = 5 + 5 + 1 = 11
4(2)+2 = 4 + 4 + 2 = 10