16Hit1600
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?

  1. A. (0, 3)Correct
  2. B. (1, 1)
  3. C. (2, 0)
  4. 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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