AlgebraMediumEquation from intercepts
Algebra practice question
A line in the xy-plane has x-intercept 6 and y-intercept 4. Which equation represents the line?
- A. y = −(2/3)x + 4Correct
- B. y = (2/3)x + 4
- C. y = −(3/2)x + 4
- D. y = −(2/3)x + 6
Answer: A. y = −(2/3)x + 4
Through (6, 0) and (0, 4): slope = (4 − 0)/(0 − 6) = −2/3, intercept 4.
Why the other answers are wrong
- B. y = (2/3)x + 4
- A positive slope would not reach the x-axis at a positive x from a positive y-intercept.
- C. y = −(3/2)x + 4
- −3/2 is the reciprocal slope (run over rise).
- D. y = −(2/3)x + 6
- 6 is the x-intercept, not the y-intercept.
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