AlgebraVery hardLinear function from its two intercepts
Algebra practice question
The graph of the linear function g in the xy-plane has x-intercept 6 and y-intercept −4. Which of the following defines g?
- A. g(x) = (2/3)x − 4Correct
- B. g(x) = (3/2)x − 4
- C. g(x) = −(2/3)x + 6
- D. g(x) = (2/3)x + 6
Answer: A. g(x) = (2/3)x − 4
The line rises 4 over a run of 6, so the slope is 2/3, and the y-intercept is −4.
Why the other answers are wrong
- B. g(x) = (3/2)x − 4
- The slope 3/2 is the reciprocal of the correct slope.
- C. g(x) = −(2/3)x + 6
- The intercepts are confused and the slope's sign is wrong.
- D. g(x) = (2/3)x + 6
- 6 is the x-intercept, not the y-intercept.
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