AlgebraHardy-intercept of a line reflected across the x-axis
Algebra practice question
In the xy-plane, line ℓ has equation 2x − 3y = 12, and line m is the reflection of line ℓ across the x-axis. What is the y-intercept of line m?
Answer: 4
Line ℓ crosses the y-axis where x = 0: −3y = 12, y = −4. Reflecting across the x-axis changes the sign of y, so line m has y-intercept 4.
Common wrong answers
- If you answered 6
- 6 is the x-intercept of ℓ, which the reflection doesn't change.
- If you answered -4
- −4 is the y-intercept of line ℓ itself.
- If you answered -6
- −6 reverses the wrong intercept.
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