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 are included in the solution set of the inequality \(-3x + 2y \geq -6\), we can test each point by substituting the \(x\) and \(y\) values into the inequality. 1. For the point (4, -5): \[ -3(4) + 2(-5) = -12 - 10 = -22 \quad (\text{not } \geq -6) \] So, this point is not included. 2. For the point (0, 0): \[ -3(0) + 2(0) = 0 \quad (\text{is } \geq -6) \] So, this point is included. 3. For the point \((3, \frac{3}{2})\): \[ -3(3) + 2\left(\frac{3}{2}\right) = -9 + 3 = -6 \quad (\text{is } \geq -6) \] So, this point is included. 4. For the point (7, -7): \[ -3(7) + 2(-7) = -21 - 14 = -35 \quad (\text{not } \geq -6) \] So, this point is not included. In summary: - (4, -5): Not included - (0, 0): Included - \((3, \frac{3}{2})\): Included - (7, -7): Not included Thus, the points included in the solution set are \((0, 0)\) and \((3, \frac{3}{2})\).