AlgebraVery hardx-intercept of a line whose intercepts are in a given ratio
Algebra practice question
In the xy-plane, line ℓ has an x-intercept that is twice its y-intercept, and ℓ passes through the point (2, 1). What is the x-intercept of line ℓ?
Answer: 4
With y-intercept b and x-intercept 2b, the line is x/(2b) + y/b = 1. At (2, 1): 2/(2b) + 1/b = 2/b = 1, so b = 2 and the x-intercept is 4.
Common wrong answers
- If you answered 1
- 1 is the y-coordinate of the given point, not an intercept.
- If you answered 2
- 2 is the y-intercept.
- If you answered 8
- 8 doubles the correct answer.
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