AlgebraVery hardIntercept in terms of a parameter
Algebra practice question
The graph of a linear function f has slope 2 and passes through the point (k, k), where k is a nonzero constant. Which expression gives f(0)?
- A. −kCorrect
- B. k
- C. 2k
- D. −2k
Answer: A. −k
f(x) = 2(x − k) + k = 2x − k, so f(0) = −k.
Why the other answers are wrong
- B. k
- k is f(k), the given value, not f(0).
- C. 2k
- 2k is the change from x = 0 to x = k, not the intercept.
- D. −2k
- −2k double-counts the slope term.
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