Determine which of the following points are included in the solution set to the following linear inequality. \[ \begin{array}{l}-5 x+4 y \geq-5\end{array} \] Answer \( \square(4,-5) \) \( \square\left(4, \frac{15}{4}\right) \) \( \square(0,0) \) \( \square(-4,4) \) \( \square(7,2) \)

To determine which points satisfy the inequality: \[ -5x + 4y \geq -5 \] we will substitute each point \((x, y)\) into the inequality and check if the condition holds. 1. **Point \((4, -5)\):** \[ -5(4) + 4(-5) = -20 - 20 = -40 \quad \text{(Not } \geq -5\text{)} \] **Does not satisfy the inequality.** 2. **Point \(\left(4, \frac{15}{4}\right)\):** \[ -5(4) + 4\left(\frac{15}{4}\right) = -20 + 15 = -5 \quad \text{(Equal to } -5\text{)} \] **Satisfies the inequality.** 3. **Point \((0, 0)\):** \[ -5(0) + 4(0) = 0 \quad \text{(Greater than } -5\text{)} \] **Satisfies the inequality.** 4. **Point \((-4, 4)\):** \[ -5(-4) + 4(4) = 20 + 16 = 36 \quad \text{(Greater than } -5\text{)} \] **Satisfies the inequality.** 5. **Point \((7, 2)\):** \[ -5(7) + 4(2) = -35 + 8 = -27 \quad \text{(Not } \geq -5\text{)} \] **Does not satisfy the inequality.** **Conclusion:** The points that **are included** in the solution set to the inequality \(-5x + 4y \geq -5\) are: - \(\left(4, \frac{15}{4}\right)\) - \((0, 0)\) - \((-4, 4)\)