Determine which of the following points are included in the solution set to the following linear inequality. \[ \begin{array}{l}-4 x+5 y \geq-3\end{array} \] Answer \( \square(0,0) \) \( \square(7,2) \) \( \square(-2,-3) \) \( \square(-2,2) \) \( \square\left(3, \frac{9}{5}\right) \)

To determine which points satisfy the inequality \(-4x + 5y \geq -3\), we can substitute each point into the inequality and check. 1. For the point \( (0, 0) \): \[ -4(0) + 5(0) \geq -3 \quad \Rightarrow \quad 0 \geq -3 \quad \text{(True)} \] 2. For the point \( (7, 2) \): \[ -4(7) + 5(2) \geq -3 \quad \Rightarrow \quad -28 + 10 \geq -3 \quad \Rightarrow \quad -18 \geq -3 \quad \text{(False)} \] 3. For the point \( (-2, -3) \): \[ -4(-2) + 5(-3) \geq -3 \quad \Rightarrow \quad 8 - 15 \geq -3 \quad \Rightarrow \quad -7 \geq -3 \quad \text{(False)} \] 4. For the point \( (-2, 2) \): \[ -4(-2) + 5(2) \geq -3 \quad \Rightarrow \quad 8 + 10 \geq -3 \quad \Rightarrow \quad 18 \geq -3 \quad \text{(True)} \] 5. For the point \( \left(3, \frac{9}{5}\right) \): \[ -4(3) + 5\left(\frac{9}{5}\right) \geq -3 \quad \Rightarrow \quad -12 + 9 \geq -3 \quad \Rightarrow \quad -3 \geq -3 \quad \text{(True)} \] Thus, the points that are included in the solution set are: - \( (0,0) \) - \( (-2,2) \) - \( \left(3, \frac{9}{5}\right) \) The answers are as follows: \( \checkmark(0,0) \) \( \checkmark(-2,2) \) \( \checkmark\left(3, \frac{9}{5}\right) \) Points \( (7,2) \) and \( (-2,-3) \) are not included in the solution set.