Find the difference quotient \( \frac{f(x+h)-f(x)}{h} \), where \( h \neq 0 \), for the function below. \[ f(x)=-9 x+5 \] Simplify your answer as much as possible. \( \frac{f(x+h)-f(x)}{h}=\square \)

To find the difference quotient for the function \( f(x) = -9x + 5 \), we will start by computing \( f(x+h) \). 1. **Calculate \( f(x+h) \)**: \[ f(x+h) = -9(x+h) + 5 = -9x - 9h + 5 \] 2. **Calculate \( f(x+h) - f(x) \)**: \[ f(x+h) - f(x) = (-9x - 9h + 5) - (-9x + 5) \] Simplifying this gives: \[ f(x+h) - f(x) = -9x - 9h + 5 + 9x - 5 = -9h \] 3. **Now plug this into the difference quotient**: \[ \frac{f(x+h) - f(x)}{h} = \frac{-9h}{h} \] Since \( h \neq 0 \), we can simplify this: \[ \frac{f(x+h) - f(x)}{h} = -9 \] Thus, the simplified difference quotient is: \[ \frac{f(x+h)-f(x)}{h} = -9 \]