AlgebraHardChecking values against a linear function defined by slope and a point
Algebra practice question
A linear function f has a slope of −2, and f(3) = 10. Which of the following must be true?
- A. f(8) = 0Correct
- B. f(0) = 10
- C. f(4) = 10
- D. f(−2) = 12
Answer: A. f(8) = 0
From f(3) = 10 with slope −2: f(x) = −2(x − 3) + 10 = −2x + 16. Then f(8) = −16 + 16 = 0.
Why the other answers are wrong
- B. f(0) = 10
- f(0) = 16, the y-intercept, not 10.
- C. f(4) = 10
- f(4) = 8: one step right lowers the value by 2.
- D. f(−2) = 12
- f(−2) = 20.
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