Find the average rate of change of \( g(x)=-3 x+5 \) between the paint \( (-1,8) \) and \( (3,-4) \)

To find the **average rate of change** of the function \( g(x) = -3x + 5 \) between the points \((-1, 8)\) and \((3, -4)\), you can use the following formula: \[ \text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a} \] where: - \( a = -1 \) and \( g(a) = 8 \) - \( b = 3 \) and \( g(b) = -4 \) **Step-by-Step Calculation:** 1. **Identify the values:** - \( g(-1) = 8 \) - \( g(3) = -4 \) 2. **Apply the formula:** \[ \text{Average Rate of Change} = \frac{g(3) - g(-1)}{3 - (-1)} = \frac{-4 - 8}{3 + 1} = \frac{-12}{4} = -3 \] **Conclusion:** The average rate of change of the function \( g(x) = -3x + 5 \) between the points \((-1, 8)\) and \((3, -4)\) is **\(-3\)**.