For the linear function f, f(3) = -2 and f(7) = 10. Which... | SAT Linear functions Question, Answer Explained

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For the linear function $f$ , $f(3) = -2$ and $f(7) = 10$ . Which equation defines $f$ ?

$f(x) = \frac{1}{3}x - 3$

$f(x) = 3x - 11$

$f(x) = 3x - 2$

$f(x) = 3x + 7$

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Answer: B

The slope is $\frac{10 - (-2)}{7 - 3} = \frac{12}{4} = 3$ . Using $f(3) = -2$ : $-2 = 3(3) + b$ , so $b = -11$ and $f(x) = 3x - 11$ . Check: $f(7) = 21 - 11 = 10$ .

Choice C uses $-2$ as the $y$ -intercept, but $-2$ is the value of $f$ at $x = 3$ , not at $x = 0$ .

Why the other choices are wrong

A. This divides the change in x by the change in f(x). The slope is 12 divided by 4, which is 3.
C. This treats -2 as the y-intercept. The value -2 is f(3), not f(0).
D. This comes from y = 3(x + 3) - 2, which uses the wrong sign in point-slope form. It should be y = 3(x - 3) - 2.

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