AlgebraMediumGraph of a linear inequality: which side is shaded
Algebra practice question
In the xy-plane, which point lies in the region defined by y ≥ 2x − 1 but NOT on its boundary line?
- A. (0, 3)Correct
- B. (1, 1)
- C. (2, 0)
- D. (3, 2)
Answer: A. (0, 3)
(0, 3): 3 ≥ −1 ✓, and 3 ≠ −1, so it's strictly inside. (1, 1) is ON the line (1 = 2 − 1).
Why the other answers are wrong
- B. (1, 1)
- (1, 1) satisfies 1 = 2(1) − 1, so it is on the boundary, which the question excludes.
- C. (2, 0)
- (2, 0): 0 ≥ 3 is false.
- D. (3, 2)
- (3, 2): 2 ≥ 5 is false.
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- Medium
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