SAT Linear functions Practice Question 16 (Hard)

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Question bank / Linear functions

Math · AlgebraHard

For the linear function $p$ , $p(1) = -3$ and $p(5) = 9$ . If $p(c) = 30$ , what is the value of $c$ ?

$8$

$11$

$12$

$84$

Show answer and explanation

Answer: C

The slope is $\frac{9 - (-3)}{5 - 1} = 3$ , so $p(x) = 3x + b$ and $-3 = 3 + b$ gives $b = -6$ . Solve $3c - 6 = 30$ : $3c = 36$ , so $c = 12$ .

Choice D is $p(30)$ , the output when the input is 30, not the input that gives an output of 30.

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