The function g is defined by g(x) = mx + b, where m and b are... | SAT Linear functions Question, Answer Explained

Math · AlgebraHard

The function $g$ is defined by $g(x) = mx + b$ , where $m$ and $b$ are constants. If $g(3) = 10$ and $g(-1) = -6$ , what is the value of $g(b)$ ?

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Answer: -10

The slope is $m = \frac{10 - (-6)}{3 - (-1)} = \frac{16}{4} = 4$ . Then $10 = 4(3) + b$ , so $b = -2$ and $g(x) = 4x - 2$ . So $g(b) = g(-2) = 4(-2) - 2 = -10$ .

Answering $-2$ gives the value of $b$ itself, not the value of the function at $x = b$ .

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