Determine which of the following points are included in the solution set to the following linear inequality. \[ \begin{array}{l}-3 x+2 y \geq-6\end{array} \] \( \begin{array}{l}\square(4,-5) \\ \text { Answer } \\ \square(0,0) \\ \square\left(3, \frac{3}{2}\right) \\ \square(7,-7)\end{array} \)

To determine which points satisfy the inequality: \[ -3x + 2y \geq -6 \] Let's evaluate each point by substituting the \( x \) and \( y \) values into the inequality. 1. **Point (4, -5):** \[ -3(4) + 2(-5) = -12 - 10 = -22 \] \[ -22 \geq -6 \quad \text{(False)} \] **Does not satisfy** the inequality. 2. **Point (0, 0):** \[ -3(0) + 2(0) = 0 \] \[ 0 \geq -6 \quad \text{(True)} \] **Satisfies** the inequality. 3. **Point \(\left(3, \frac{3}{2}\right)\):** \[ -3(3) + 2\left(\frac{3}{2}\right) = -9 + 3 = -6 \] \[ -6 \geq -6 \quad \text{(True)} \] **Satisfies** the inequality. 4. **Point (7, -7):** \[ -3(7) + 2(-7) = -21 - 14 = -35 \] \[ -35 \geq -6 \quad \text{(False)} \] **Does not satisfy** the inequality. ### Summary of Points: - ☐ (4, -5) - ☑ (0, 0) - ☑ \(\left(3, \frac{3}{2}\right)\) - ☐ (7, -7) **Points that satisfy the inequality:** \((0, 0)\) and \(\left(3, \frac{3}{2}\right)\).