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The problem is asking for the **slope of the tangent line** to the function at a specific point. Here's the function and point given:

**Function**: \( f(x) = 3 - 5x \)

**Point**: \( (-1, 8) \)

### Steps to find the slope of the tangent line:

1. **Differentiate the function** to find its slope at any point:
   \[
   f(x) = 3 - 5x
   \]
   The derivative \( f'(x) \), which represents the slope of the tangent line, is:
   \[
   f'(x) = -5
   \]
   Since the derivative is a constant, the slope of the tangent line is the same at any point.

2. **Conclusion**: The slope of the tangent line at the point \( (-1, 8) \) is **-5**.

Would you like a more detailed explanation or any clarification?

Here are 5 related questions you might find helpful:

1. What is the general process for finding the slope of a tangent line for a quadratic function?
2. How would the method change if the function were non-linear, like \( f(x) = x^2 \)?
3. Can you explain the geometric interpretation of the slope of a tangent line?
4. What does it mean for a tangent line to be horizontal?
5. How can we verify that the point \( (-1, 8) \) lies on the graph of the function?

**Tip**: The slope of a tangent line is always the value of the derivative at the given point. So, finding derivatives is key to understanding rates of change!

Find the slope of the tangent line to the graph of the function f(x) = 3 - 5x at the point (-1, 8).

Learn how to find the slope of the tangent line for the linear function f(x) = 3 - 5x at the point (-1, 8). This problem covers key concepts in differentiation and tangent lines. Suitable for students in Grades 10-12.

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