AlgebraHardLine through two points with the same x
Algebra practice question
The points (2, −3) and (2, 7) both lie on line m in the xy-plane. Which statement about line m is true?
- A. Its equation is x = 2, and its slope is undefined.Correct
- B. Its slope is 0.
- C. Its equation is y = 2.
- D. It passes through the origin.
Answer: A. Its equation is x = 2, and its slope is undefined.
Both points have x = 2, so the line is vertical: every point on it has x = 2. A vertical line's slope is undefined (its run is zero).
Why the other answers are wrong
- B. Its slope is 0.
- A slope of 0 belongs to a horizontal line; this line is vertical.
- C. Its equation is y = 2.
- y = 2 is horizontal, and neither given point has y = 2.
- D. It passes through the origin.
- The origin has x = 0, not 2.
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