AlgebraHardx-intercept of a line built from another line's features
Algebra practice question
In the xy-plane, line ℓ has equation 3x + 5y = 30. Line k has the same y-intercept as line ℓ and twice its slope. What is the x-intercept of line k?
Answer: 5
Line ℓ: y = −(3/5)x + 6, so its y-intercept is 6 and slope −3/5. Line k: y = −(6/5)x + 6. Set y = 0: x = 5.
Common wrong answers
- If you answered 10
- 10 is the x-intercept of line ℓ, not k.
- If you answered 20
- 20 doubles ℓ's x-intercept instead of its slope.
- If you answered -5
- −5 has the wrong sign.
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