AlgebraMediumEquation of a line after doubling both intercepts
Algebra practice question
In the xy-plane, line ℓ has equation 5x + 2y = 20. A second line has both its x-intercept and its y-intercept twice those of line ℓ. Which of the following is an equation of the second line?
- A. 5x + 2y = 40Correct
- B. 10x + 4y = 20
- C. 5x + 2y = 10
- D. 10x + 4y = 40
Answer: A. 5x + 2y = 40
Line ℓ has intercepts 4 and 10. Doubling both to 8 and 20 gives 5x + 2y = 40 (check: x = 8 when y = 0, y = 20 when x = 0).
Why the other answers are wrong
- B. 10x + 4y = 20
- 10x + 4y = 20 halves the intercepts.
- C. 5x + 2y = 10
- 5x + 2y = 10 halves the intercepts.
- D. 10x + 4y = 40
- 10x + 4y = 40 is the same line as ℓ.
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