Draw the graph of your function

Then draw a straight line through the function. Do this on graph paper if you need to so that you can draw a line through points that you can see the value of. I have attached a graph that I made to show you what I mean by this.

SLOPE-AVERAGE RATE OF CHANGE.doc
It is a parabola with its vertex at the origin. "a" & "b" are x-values somewhere on the graph. f(a) and f(b) are the y-values associated with those x-values.

The average rate of change of a function is the slope of a secant line of the function. A secant line is a straight line that goes through the graph of the function intersecting at two separate points.

The slope of the secant line is:

OR

So, choose any value of x, let's say x=2. Now, to find the y-value associated with that x-value, plug the x-value into your function.

which can also be written as

So,

or

So when x=2 on the graph of this function, y=4

Does that make sense?

So,

a = 2

f(2) = 4

Now pick another value on your function, let's say x = -1

Plug -1 into

, you get

So,

b = -1

f(b) = 1

So from your problem:

So, the average slope of your function is m = 1

Does that help you understand now?