To determine which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we will substitute the x-values from each point into the equation \( y = 25x + 1 \) and check if the y-value of the point is less than or equal to the result.
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For the point (10, 5.5): \[ y = 25(10) + 1 = 250 + 1 = 251 \] \[ 5.5 \leq 251 \quad \text{(True)} \]
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For the point (−10, 6): \[ y = 25(-10) + 1 = -250 + 1 = -249 \] \[ 6 \leq -249 \quad \text{(False)} \]
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For the point (10, 6): \[ y = 25(10) + 1 = 250 + 1 = 251 \] \[ 6 \leq 251 \quad \text{(True)} \]
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For the point (10, 4): \[ y = 25(10) + 1 = 250 + 1 = 251 \] \[ 4 \leq 251 \quad \text{(True)} \]
The points (10, 5.5), (10, 6), and (10, 4) are all part of the solution set for the inequality \( y \leq 25x + 1 \), while the point (−10, 6) is not.
So, the points that satisfy the inequality are:
- (10, 5.5)
- (10, 6)
- (10, 4)
Answer: (10, 5.5), (10, 6), and (10, 4) are part of the solution set.