AlgebraVery hardIntercept in terms of a parameter
Algebra practice question
For a nonzero constant a, the graph of the linear function f passes through the points (a, 2a) and (3a, 8a). Which expression gives f(0)?
- A. −aCorrect
- B. a
- C. 2a
- D. −3a
Answer: A. −a
Slope = (8a − 2a)/(3a − a) = 3. Then f(x) = 3x + c with 3a + c = 2a, so c = −a.
Why the other answers are wrong
- B. a
- Sign error in solving 3a + c = 2a.
- C. 2a
- 2a is f(a), not f(0).
- D. −3a
- −3a comes from using slope 3 with the point (a, 0).
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