For the linear function g, the value of g(x) increases by 15... | SAT Linear functions Question, Answer Explained

Math · AlgebraMedium

For the linear function $g$ , the value of $g(x)$ increases by $15$ each time $x$ increases by $6$ , and $g(0) = -4$ . Which equation defines $g$ ?

$g(x) = \frac{2}{5}x - 4$

$g(x) = \frac{5}{2}x - 4$

$g(x) = 9x - 4$

$g(x) = 15x - 4$

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Answer: B

The slope is the change in $g(x)$ divided by the change in $x$ : $\frac{15}{6} = \frac{5}{2}$ . The $y$ -intercept is $g(0) = -4$ . So $g(x) = \frac{5}{2}x - 4$ .

Choice A divides $6$ by $15$ , which puts the change in $x$ over the change in $g(x)$ .

Why the other choices are wrong

A. This divides the change in x by the change in g(x). Slope is the change in g(x) divided by the change in x.
C. This subtracts 6 from 15. Slope is a ratio, so divide 15 by 6.
D. 15 is the change in g(x) when x increases by 6, not when x increases by 1.

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