To determine which of the given points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we can substitute each point into the inequality.
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Check (10, 5.5): \[ y = 5.5, \quad x = 10 \] Substitute into the inequality: \[ 5.5 \leq \frac{2}{5}(10) + 1 \] \[ 5.5 \leq 4 + 1 \] \[ 5.5 \leq 5 \] False
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Check (10, 6): \[ y = 6, \quad x = 10 \] Substitute into the inequality: \[ 6 \leq \frac{2}{5}(10) + 1 \] \[ 6 \leq 4 + 1 \] \[ 6 \leq 5 \] False
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Check (10, 4): \[ y = 4, \quad x = 10 \] Substitute into the inequality: \[ 4 \leq \frac{2}{5}(10) + 1 \] \[ 4 \leq 4 + 1 \] \[ 4 \leq 5 \] True
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Check (−10, 6): \[ y = 6, \quad x = -10 \] Substitute into the inequality: \[ 6 \leq \frac{2}{5}(-10) + 1 \] \[ 6 \leq -4 + 1 \] \[ 6 \leq -3 \] False
The only point that is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \) is (10, 4).