AlgebraHardSum of a line's intercepts
Algebra practice question
The graph of f(x) = 3x + k passes through the point (2, 11). What is the sum of the x-intercept and the y-intercept of the graph of f?
- A. 10/3Correct
- B. 20/3
- C. 5
- D. −10/3
Answer: A. 10/3
From f(2) = 11, k = 5. The y-intercept is 5; the x-intercept solves 3x + 5 = 0, giving −5/3. Their sum is 5 − 5/3 = 10/3.
Why the other answers are wrong
- B. 20/3
- 20/3 comes from adding 5 + 5/3 — the x-intercept is negative: −5/3.
- C. 5
- 5 is only the y-intercept; the question asks for the sum with the x-intercept −5/3.
- D. −10/3
- −10/3 reverses both signs; the y-intercept 5 outweighs the x-intercept −5/3.
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