To determine which of the given points satisfies the inequality \( y \leq \frac{2}{5}x + 1 \), we need to plug in the x-coordinates of each point into the inequality and see if the corresponding y-coordinates satisfy it.
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Point (10, 4):
- Calculate the right-hand side: \[ \frac{2}{5}(10) + 1 = 4 + 1 = 5 \]
- Check the inequality: \[ 4 \leq 5 \quad \text{(True)} \]
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Point (−10, 6):
- Calculate the right-hand side: \[ \frac{2}{5}(-10) + 1 = -4 + 1 = -3 \]
- Check the inequality: \[ 6 \leq -3 \quad \text{(False)} \]
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Point (10, 6):
- Calculate the right-hand side: \[ \frac{2}{5}(10) + 1 = 5 + 1 = 6 \]
- Check the inequality: \[ 6 \leq 6 \quad \text{(True)} \]
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Point (10, 5.5):
- Calculate the right-hand side: \[ \frac{2}{5}(10) + 1 = 5 + 1 = 6 \]
- Check the inequality: \[ 5.5 \leq 6 \quad \text{(True)} \]
Summary:
- (10, 4) → true
- (−10, 6) → false
- (10, 6) → true
- (10, 5.5) → true
Therefore, the points (10, 4), (10, 6), and (10, 5.5) are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \). The only point that is not in the solution set is (−10, 6).
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