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Let's go through the problem step by step.

We are given the function:
\[
f(x) = 8 - 7x
\]
We need to find:

1. \( f(a) \)
2. \( f(a + h) \)
3. The difference quotient: 
\[
\frac{f(a + h) - f(a)}{h}
\]

### 1. Finding \( f(a) \):
Substitute \( x = a \) into the function \( f(x) = 8 - 7x \):
\[
f(a) = 8 - 7a
\]

### 2. Finding \( f(a + h) \):
Substitute \( x = a + h \) into the function:
\[
f(a + h) = 8 - 7(a + h) = 8 - 7a - 7h
\]

### 3. Finding the difference quotient:
\[
\frac{f(a + h) - f(a)}{h}
\]
Substitute the expressions for \( f(a + h) \) and \( f(a) \):
\[
\frac{(8 - 7a - 7h) - (8 - 7a)}{h}
\]
Simplify the numerator:
\[
= \frac{8 - 7a - 7h - 8 + 7a}{h} = \frac{-7h}{h}
\]
Cancel out \( h \) (since \( h \neq 0 \)):
\[
= -7
\]

### Final answers:
1. \( f(a) = 8 - 7a \)
2. \( f(a + h) = 8 - 7a - 7h \)
3. \( \frac{f(a + h) - f(a)}{h} = -7 \)

Would you like further details or clarifications on any part of this solution?

Here are 5 related questions for practice:
1. What is the derivative of the function \( f(x) = 8 - 7x \)?
2. Find the difference quotient for the function \( f(x) = x^2 - 4x \).
3. What is the physical interpretation of the difference quotient in real-world problems?
4. How does the difference quotient relate to the slope of a secant line?
5. How would the difference quotient change if we used a quadratic function?

**Tip:** The difference quotient is the foundation of the derivative. Understanding how it works will help you with concepts in calculus, especially when studying limits and instantaneous rates of change.

Find f(a), f(a + h), and the difference quotient [f(a + h) - f(a)] / h, where f(x) = 8 - 7x.

Solve for f(a), f(a + h), and the difference quotient for the linear function f(x) = 8 - 7x. This example covers the fundamentals of difference quotients and function evaluation, suitable for Pre-Calculus students.

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