To determine which of the following points is part of the solution set for the inequality \( y \geq 3x - 1 \), we will substitute the x-coordinates of each point into the equation \( y = 3x - 1 \) and check if the corresponding y-values satisfy the inequality.
-
For the point (1, 1): \[ y = 3(1) - 1 = 3 - 1 = 2 \] Check the inequality: \[ 1 \geq 2 \quad \text{(False)} \]
-
For the point (2, 5): \[ y = 3(2) - 1 = 6 - 1 = 5 \] Check the inequality: \[ 5 \geq 5 \quad \text{(True)} \]
-
For the point (-2.5, -9): \[ y = 3(-2.5) - 1 = -7.5 - 1 = -8.5 \] Check the inequality: \[ -9 \geq -8.5 \quad \text{(False)} \]
-
For the point (-1, -5): \[ y = 3(-1) - 1 = -3 - 1 = -4 \] Check the inequality: \[ -5 \geq -4 \quad \text{(False)} \]
The only point that satisfies the inequality \( y \geq 3x - 1 \) is \( (2, 5) \). Therefore, the correct answer is:
(2, 5)