AlgebraVery hardIntercept from a fixed ratio and a point
Algebra practice question
In the xy-plane, a line crosses the x-axis at (a, 0) and the y-axis at (0, 2a), where a ≠ 0, and passes through the point (3, 4). What is the value of a?
Answer: 5
The slope is (2a − 0)/(0 − a) = −2, so y = −2x + 2a. Substituting (3, 4): 4 = −6 + 2a, so a = 5.
Common wrong answers
- If you answered 2
- 2 comes from solving 2a − 6 = 4 as 2a = 4, a slip.
- If you answered 10
- 10 is 2a, the y-intercept.
- If you answered -1
- −1 uses slope +2.
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