To determine which ordered pairs are solutions for the inequality \( y > -2x + 8 \), we can substitute the \( x \) values of each ordered pair into the inequality and see if the resulting \( y \) value is greater than the right-hand side of the inequality.
-
For (2, -12): \[ y > -2(2) + 8 \] \[ -12 > -4 + 8 \] \[ -12 > 4 \quad \text{(False)} \]
-
For (-1, 14): \[ y > -2(-1) + 8 \] \[ 14 > 2 + 8 \] \[ 14 > 10 \quad \text{(True)} \]
-
For (4, 2): \[ y > -2(4) + 8 \] \[ 2 > -8 + 8 \] \[ 2 > 0 \quad \text{(True)} \]
Based on these calculations, the ordered pairs that are solutions for the inequality \( y > -2x + 8 \) are:
- \((-1, 14)\)
- \((4, 2)\)
Thus, the correct answers are (-1, 14) and (4, 2).