To determine which points are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we first need to evaluate each point by substituting the x-value into the equation \( y = \frac{2}{5}x + 1 \) and then checking if the y-value of each point is less than or equal to the result.
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Point (5, 3):
- Calculate \( y = \frac{2}{5}(5) + 1 \): \[ y = 2 + 1 = 3 \]
- Since \( 3 \leq 3 \), the point (5, 3) is in the solution set.
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Point (10, 4):
- Calculate \( y = \frac{2}{5}(10) + 1 \): \[ y = 4 + 1 = 5 \]
- Since \( 4 \leq 5 \), the point (10, 4) is in the solution set.
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Point (10, 6):
- Calculate \( y = \frac{2}{5}(10) + 1 \): \[ y = 5 \]
- Since \( 6 \leq 5 \) is false, the point (10, 6) is not in the solution set.
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Point (10, 5.5):
- Calculate \( y = \frac{2}{5}(10) + 1 \): \[ y = 5 \]
- Since \( 5.5 \leq 5 \) is false, the point (10, 5.5) is not in the solution set.
In summary, the points that are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \) are:
- (5, 3)
- (10, 4)
So the answers are:
- (5, 3)
- (10, 4)