Let I be an interval of the real line prove that the following function increases on that line

Let I be an interval of the real line, that is to say, let I be a line somewhere on the line from negative infinity to positive infinity. Also let I be a subset of the domain of f (a function). It can be said that f is increasing on I if and only if for all x,y that is an element of I, if x < y then f(x) < f(y).

Prove that f is increasing on the set of real numbers where f(x)= 3x - 7

Suppose that x < y then 3x < 3y and therefore 3x-7 < 3y-7, and thus f(x) < f(y), so f is increasing on the interval I and the set of real numbers.