Frozen Warnings

Edit: Nevermind, I understand now.. x1 is the leftmost x on the graph, x2 is the rightmost.  So in order to be inceasing, x1 has to be less than x2.                

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I'm working with continuity of functions and don't fully understand my book's explaination:

Criteria for Increasing, Decreasing and Constant on an interval.

Suppose that a function f is defined over an interval I.

(a) f increases on I if, whenever x1 < x2, f(x1) < f(x2);
(a) f decreases on I if, whenever x1 < x2, f(x1) > f(x2);
(a) f is constant on I if, whenever x1 < x2, f(x1) = f(x2);

So, given:
f(x)=mx+b, m>0 -> increasing
f(x)=mx+b, m<0 -> decreasing

How do I relate the previous two statements to my book's criteria above?

The way I learned from my last class is that if a line goes up from left to right, it's an increasing function. Lines that go down from left to right are decreasing.  But clearly, the authors want me to think about this more deeply.