AlgebraMediumLine that meets a given line at exactly one point
Algebra practice question
In the xy-plane, which of the following is an equation of a line that intersects the line y = 2x + 1 at exactly one point?
- A. y = 3x + 1Correct
- B. y = 2x − 1
- C. y = 2x + 1
- D. 2y = 4x + 2
Answer: A. y = 3x + 1
Lines with different slopes meet exactly once; y = 3x + 1 has slope 3, not 2.
Why the other answers are wrong
- B. y = 2x − 1
- Slope 2 with a different intercept: parallel, so no intersection.
- C. y = 2x + 1
- The same line, so infinitely many common points.
- D. 2y = 4x + 2
- 2y = 4x + 2 is the same line as y = 2x + 1.
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