2003 AMC 12B Problem 9

Attempt Problem 9 of the 2003 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Let

f

be a linear function for which

f(6) - f(2) = 12.

What is

f(12) - f(2)?

12

18

24

30

36

A linear function has a constant rate of change (slope)

The slope is

\dfrac{f(6) - f(2)}{6 - 2},

and the answer is that slope times

12 - 2

The slope of

f

\frac{f(6) - f(2)}{6 - 2} = \frac{12}{4} = 3.

Therefore

f(12) - f(2) = 3(12 - 2) = 30.

Thus, the correct answer is D.

Problem 9 in other years