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Linear Functions

SAT Math· difficulty 4/5

The function f(x)=ax+bf(x) = ax + b satisfies the table:

<table> <thead> <tr> <th>$x$</th> <th>$-1$</th> <th>$2$</th> </tr> </thead> <tbody><tr> <td>$f(x)$</td> <td>$4$</td> <td>$-5$</td> </tr> <tr> <td>What is $a + b$?</td> <td></td> <td></td> </tr> </tbody></table>
  • A

    −3-3

  • B

    22

  • C

    00

  • D

    −2-2

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Explanation

Slope a=(−5−4)/(2−(−1))=−3a = (-5 - 4)/(2 - (-1)) = -3. f(−1)=−a+b=3+b=4f(-1) = -a + b = 3 + b = 4, b=1b = 1. a+b=−2a + b = -2.

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