To determine which points are part of the solution set for the inequality \( y < \frac{2}{5}x + 1 \), we need to evaluate each given point by substituting the \( x \) value into the equation \( y = \frac{2}{5}x + 1 \) and then checking if the \( y \) value of the point is less than the calculated \( y \) value.
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Point A: (10, 4) \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Check: \( 4 < 5 \) (True)
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Point B: (10, 6) \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Check: \( 6 < 5 \) (False)
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Point C: (5, 3) \[ y = \frac{2}{5}(5) + 1 = 2 + 1 = 3 \] Check: \( 3 < 3 \) (False)
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Point D: (10, 5.5) \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Check: \( 5.5 < 5 \) (False)
Now let's summarize:
- A. (10, 4) is part of the solution set.
- B. (10, 6) is not part of the solution set.
- C. (5, 3) is not part of the solution set.
- D. (10, 5.5) is not part of the solution set.
Thus, the only point that is part of the solution set is A. (10, 4).
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