The given function is \( f(x) = 5x - 1 \). This is a linear function, where the slope is 5 and the y-intercept is -1. Let's explore some important properties and insights about this function:

### Key Properties:
1. **Slope (m):** The slope of the line is 5, which means for every unit increase in \( x \), the value of \( f(x) \) increases by 5.
2. **Y-intercept (b):** The y-intercept is -1, meaning that the graph of the function crosses the y-axis at the point (0, -1).
3. **X-intercept:** To find the x-intercept, set \( f(x) = 0 \) and solve for \( x \):
   \[
   0 = 5x - 1
   \]
   Solving this gives \( x = \frac{1}{5} \). So the x-intercept is \( \left(\frac{1}{5}, 0\right) \).
4. **Graph:** The graph of this function is a straight line with a positive slope. It rises as \( x \) increases.

### Example:
If \( x = 2 \), then:
\[
f(2) = 5(2) - 1 = 10 - 1 = 9
\]

Let me know if you need more details or have any questions!

Here are 5 questions based on this function:
1. What is the value of \( f(x) \) when \( x = -1 \)?
2. How would you find the slope from two points on the graph of \( f(x) \)?
3. What happens to the graph of \( f(x) \) if we change the slope from 5 to another value?
4. How would you solve \( f(x) = 14 \) for \( x \)?
5. What would the graph look like if we add a constant term to \( f(x) \)?

**Tip:** The slope of a linear function gives the rate of change of the function with respect to \( x \).

Understand how to analyze the linear function f(x) = 5x - 1. This tutorial explains the slope, y-intercept, and x-intercept, with examples and graphing tips. Ideal for students in Grades 6-8 learning linear functions in algebra.

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