To find out how fast a tree grows, you can measure its trunk. a giant red oak's diameter was 248 inches in 1965. the tree's diameter had grown to 251 inches in 2005. find the average rate of change in the diameter of the tree per year.

Any times you see the phrase: "Rate of Change", or even sometimes just the word "Rate" think slope. 

The word slope is just a fancy word that means the rate of change. 

Rate of Change is just a fancy phrase meaning how much does something change over some amount of time. 
So in this case our rate of change will have the units of inches per year. 

Let's get to the problem at hand! 
We'll need to find slope / the rate of change (the two are interchangeable with each other).
Let's go over the formula for slope:

m = (y2 - y1) / (x2 - x1) 

First we will need to label each of the "coordinated points (the two numbers that go together in a pair)" with either (x1,y1) or (x2,y2). 

A Giant Red Oak's diameter in 1965 was 248 inches. Keep in mind time is ALWAYS going to be X in rate of change problems (and most all problems for that matter).  

(1965,248) 
(X1,Y2)

(2005,251)
(X2,Y2)

Plug in the values into the equation!
m = (y2 - y1) / (x2 - x1)
m = (251 - 248) / (2005 - 1965) 
m = (3) / (40)

Type that into a calculator to get a decimal value over 1.
m = 0.075 inches per 1 year. 
Or... 

m = 0.075in / 1 year