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

"Why?" in math has various meanings.

Let's solve

5x +1 > 4x + 1

That's easily solved,

5x - 4x > 1 - 1

x > 0

Since x>1 is included in x>0, it's in the solution set to the above inequality, so all such x make the inequality true.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.