The problem asks you to find the difference quotient for the given function:

$f(x) = -10x - 13$

The difference quotient is given by the formula:

$\frac{f(x+h) - f(x)}{h}$

To solve this, follow these steps:

1. Find $f(x + h)$:
   Substitute $x + h$ into the function $f(x)$.
   So, $f(x + h) = -10(x + h) - 13 = -10x - 10h - 13$

2. Substitute $f(x + h)$ and $f(x)$ into the difference quotient formula:

   We already know that $f(x) = -10x - 13$. Therefore: $\frac{f(x+h) - f(x)}{h} = \frac{(-10x - 10h - 13) - (-10x - 13)}{h}$

3. Simplify the expression:

   = \frac{-10h}{h}$$

4. Simplify further: $= -10$

So, the difference quotient for this function is $-10$.

Would you like further explanation or have any questions about this process? Here are some related questions:

1. What is the significance of the difference quotient in calculus?
2. How would the difference quotient change if the function were quadratic, e.g., $f(x) = x^2$?
3. Can you find the derivative of this function using the limit of the difference quotient?
4. What happens when you try to find the difference quotient for a constant function like $f(x) = 5$?
5. How would you calculate the difference quotient for a function involving trigonometric terms?

Tip: The difference quotient is a key concept when working with derivatives and approximating the rate of change of a function!