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The image contains a mathematical problem asking to find and simplify the expression \(\frac{g(x+h) - g(x)}{h}\) for the given function \(g(x)\).

The function given is:

\[
g(x) = 7x - 5
\]

We are asked to find and simplify the expression:

\[
\frac{g(x+h) - g(x)}{h}
\]

### Steps to Solve:

1. **Substitute \(g(x)\) and \(g(x+h)\)**:
   - First, compute \(g(x+h)\):
     \[
     g(x+h) = 7(x+h) - 5 = 7x + 7h - 5
     \]
   - Now, substitute both \(g(x+h)\) and \(g(x)\) into the difference quotient:
     \[
     \frac{g(x+h) - g(x)}{h} = \frac{(7x + 7h - 5) - (7x - 5)}{h}
     \]

2. **Simplify the Expression**:
   - Simplify the numerator:
     \[
     \frac{(7x + 7h - 5) - (7x - 5)}{h} = \frac{7x + 7h - 5 - 7x + 5}{h} = \frac{7h}{h}
     \]
   - Since \(h \neq 0\), cancel out \(h\) in the numerator and denominator:
     \[
     \frac{7h}{h} = 7
     \]

So, the simplified expression is **7**.

---

Would you like further details or have any questions? Here are some related questions to explore further:

1. How does this problem relate to the concept of the derivative?
2. What is the geometric interpretation of the expression \(\frac{g(x+h) - g(x)}{h}\) in the context of this problem?
3. How would the answer change if the function \(g(x)\) were quadratic instead of linear?
4. What does the result \(7\) tell you about the slope of the function \(g(x)\)?
5. How can this concept be extended to functions with more complex expressions?

**Tip:** This expression is the definition of the derivative. For linear functions, the derivative is the coefficient of \(x\), which is the slope of the line.

Find and simplify the expression \(\frac{g(x+h) - g(x)}{h}\) for the given function \(g(x) = 7x - 5\).

Learn how to find and simplify the difference quotient \(\frac{g(x+h) - g(x)}{h}\) for the linear function \(g(x) = 7x - 5\). This problem introduces the concept of derivatives and provides a step-by-step solution suitable for students in Grades 11-12.

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