To determine which points satisfy the inequality represented by the shaded region on the graph, we first need to clarify the boundaries formed by the dotted lines.
From your description:
- The first dotted line runs through points (0, -1), (-1, -3), and (-2, -5) and goes downward. This line appears to be decreasing and likely has a negative slope.
- The second dotted line runs through points (0.5, 0), (1, 1), (1.5, 2), (2, 3), and (3, 5) and goes upward. This line appears to be increasing and likely has a positive slope.
Analyzing the points given:
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(-2, -2): This point is to the left of the downward line and above the upward line, thus it is inside the shaded area.
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(2, -2): This point is above the upward line and not below the downward line, thus it is not in the shaded area.
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(-1, 0): This point is to the right of the downward line and above the upward line, thus it is not in the shaded area.
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(-1, -3): This point is exactly on the downward dotted line (which represents the boundary), thus it is not in the shaded area (since shaded areas typically exclude the boundary).
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(-3, 3): This point is above the upward line and to the left of the downward line, thus it is not in the shaded area.
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(4, 4): This point is above the upward line, thus it is not in the shaded area.
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(-4, 10): This point is to the left of the downward line and above the upward line, thus it is also inside the shaded area.
Conclusion
The points that would make the inequality true, meaning they are within the shaded area, are:
- (-2, -2)
- (-4, 10)
Thus, the correct selections are:
- (-2, -2)
- (-4, 10)