SAT Linear functions Practice Question 8 (Medium)

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Math · AlgebraMedium

For the linear function $f$ , $f(2) = 7$ and $f(6) = 19$ . What is the value of $f(10)$ ?

$25$

$27$

$31$

$38$

Show answer and explanation

Answer: C

The slope is $\frac{19 - 7}{6 - 2} = 3$ . From $x = 6$ to $x = 10$ , $x$ increases by 4, so $f$ increases by $3 \cdot 4 = 12$ . Thus $f(10) = 19 + 12 = 31$ .

Choice D assumes $f(10)$ is double $f(6)$ , but a linear function with a nonzero intercept is not proportional.

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