To determine which of the given points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we need to substitute the x-coordinate of each point into the equation \( y = \frac{2}{5}x + 1 \) to find the corresponding y-value and then check if the actual y-value of the point is less than or equal to this calculated value.
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Point (10, 6): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Here, \( 6 \leq 5 \) is false.
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Point (-10, 6): \[ y = \frac{2}{5}(-10) + 1 = -4 + 1 = -3 \] Here, \( 6 \leq -3 \) is false.
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Point (10, 4): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Here, \( 4 \leq 5 \) is true.
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Point (10, 5.5): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Here, \( 5.5 \leq 5 \) is false.
The only point that satisfies the inequality \( y \leq \frac{2}{5}x + 1 \) is:
(10, 4).