The following is a partial table of values for

Hello!

The average rate of change is dy/dx (the change of the function divided by the change of x).Here it is

(-3.9 - 1.9)/(15 - 10) = -5.8/5 = -11.6/10 = -1.16.

To estimate f(13) we suppose f(x) is linear between x=10 and x=15.Then f(13) approx = f(10) + (dx from 10 to 13) * (the average rate). Substitute our numbers:

f(13) approx = f(10) + (13-10)*(-1.16) = 1.9 - 3*1.16 = 1.9 - 3.48 = -1.58 approx = -1.6

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