To determine which points are part of the solution set for the inequality \(y \geq 3x - 1\), we can substitute each point into the inequality and check if it holds true.
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For the point \((1, 1)\): \[ y \geq 3x - 1 \implies 1 \geq 3(1) - 1 \implies 1 \geq 3 - 1 \implies 1 \geq 2 \quad (\text{False}) \]
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For the point \((-1, -5)\): \[ y \geq 3x - 1 \implies -5 \geq 3(-1) - 1 \implies -5 \geq -3 - 1 \implies -5 \geq -4 \quad (\text{False}) \]
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For the point \((2, 5)\): \[ y \geq 3x - 1 \implies 5 \geq 3(2) - 1 \implies 5 \geq 6 - 1 \implies 5 \geq 5 \quad (\text{True}) \]
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For the point \((-2.5, -9)\): \[ y \geq 3x - 1 \implies -9 \geq 3(-2.5) - 1 \implies -9 \geq -7.5 - 1 \implies -9 \geq -8.5 \quad (\text{False}) \]
The only point that satisfies the inequality \(y \geq 3x - 1\) is \((2, 5)\). Therefore, the point \((2, 5)\) is a part of the solution set for the inequality.
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