To determine which points are 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 \( y = \frac{2}{5}x + 1 \) and check if the corresponding y-value is greater than or equal to the result.
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For the point (10, 6): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Since \( 6 \leq 5 \) is false, this point is not in the solution set.
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For the point (10, 4): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Since \( 4 \leq 5 \) is true, this point is in the solution set.
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For the point (5, 3): \[ y = \frac{2}{5}(5) + 1 = 2 + 1 = 3 \] Since \( 3 \leq 3 \) is true, this point is in the solution set.
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For the point (10, 5.5): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Since \( 5.5 \leq 5 \) is false, this point is not in the solution set.
In conclusion, the points that are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \) are:
- (10, 4)
- (5, 3)