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Linear Functions

SAT Math· difficulty 5/5

The linear function ff satisfies f(2)=5f(2) = 5 and f(a)=5a−1f(a) = 5a - 1. If the slope of ff is 22, what is the value of aa?

  • A

    3

  • B

    2

  • C

    23\frac{2}{3}

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  • D

    43\frac{4}{3}

Explanation

With slope 22 and f(2)=5f(2) = 5: f(x)=2x+1f(x) = 2x + 1. So f(a)=2a+1=5a−1f(a) = 2a + 1 = 5a - 1, giving 3a=23a = 2 and a=23a = \frac{2}{3}.

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