2003 AMC 12B Problems/Problem 9

Problem 9

Let $f$ be a linear function for which $f(6) - f(2) = 12.$ What is $f(12) - f(2)?$

$\text {(A) } 12 \qquad \text {(B) } 18 \qquad \text {(C) } 24 \qquad \text {(D) } 30 \qquad \text {(E) } 36$

Since $f$ is a linear function with slope $m$ ,

$m = \frac{f(6) - f(2)}{\Delta x} = \frac{12}{6 - 2} = 3$

$f(12) - f(2) = m \Delta x = 4(12 - 2) = 30 \Rightarrow \text (D)$