Why will the value of y for the function y equals 5x + 1 always be greater than that of y equals 4x + 1 with X greater than 1?

Because 5 times any number > 1 will always be greater then 4 times any number > 1.

You mean

the linear equations, 5x-y+1=0,4x-y+1=0

the slopes are 5 and 4 respectively.

it is clear that slope of first equation is greater that is it has a steeper graph therefore it Will always be greater than the other for x > 1

the same can be done by calculus; differentiation.

note y=5x+1 is always greater than y=4x+1 for all x>1