AlgebraVery hardIntercept relationship through a point
Algebra practice question
A line passes through the point (3, −2), and its x-intercept is twice its y-intercept (both nonzero). What is the y-coordinate of the line's y-intercept? (Enter your answer as a fraction or decimal.)
Answer: -1/2 or -0.5
With y-intercept b and x-intercept 2b, the line is x/(2b) + y/b = 1. Substituting (3, −2): 3/(2b) − 2/b = 1. Over the common denominator 2b this is (3 − 4)/(2b) = 1, so 2b = −1 and b = −1/2.
Common wrong answers
- If you answered -1
- Combine the fractions over 2b: 3/(2b) − 4/(2b) = −1/(2b) = 1, so 2b = −1 and b = −1/2.
- If you answered 1/2
- Watch the sign: −1/(2b) = 1 forces b negative.
- If you answered -2
- −2 is the y-coordinate of the given point, not the intercept.
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