To find which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we will substitute each point into the inequality and see if it holds true.
-
For the point \( (10, 4) \): \[ y \leq 25x + 1 \implies 4 \leq 25(10) + 1 \implies 4 \leq 250 + 1 \implies 4 \leq 251 \quad \text{(True)} \]
-
For the point \( (10, 5.5) \): \[ y \leq 25x + 1 \implies 5.5 \leq 25(10) + 1 \implies 5.5 \leq 250 + 1 \implies 5.5 \leq 251 \quad \text{(True)} \]
-
For the point \( (10, 6) \): \[ y \leq 25x + 1 \implies 6 \leq 25(10) + 1 \implies 6 \leq 250 + 1 \implies 6 \leq 251 \quad \text{(True)} \]
-
For the point \( (-10, 6) \): \[ y \leq 25x + 1 \implies 6 \leq 25(-10) + 1 \implies 6 \leq -250 + 1 \implies 6 \leq -249 \quad \text{(False)} \]
From our calculations:
- \( (10, 4) \) is part of the solution set.
- \( (10, 5.5) \) is part of the solution set.
- \( (10, 6) \) is also part of the solution set.
- \( (-10, 6) \) is not part of the solution set.
Therefore, the points \( (10, 4) \), \( (10, 5.5) \), and \( (10, 6) \) are all within the solution set for the inequality \( y \leq 25x + 1 \).