https://file.aiquickdraw.com/mathbot/file/1726905338730fnezh4zu.jpg

In this image, you are tasked with graphing the linear function \( f(x) = ax \) for three different values of \( a \) on the same set of axes: 

1. \( a = \frac{1}{8} \)
2. \( a = 1 \)
3. \( a = 8 \)

These represent three different slopes of the function \( f(x) = ax \).

### Explanation:

- **\( a = \frac{1}{8} \)**: This represents a line with a very shallow slope. The line will rise very slowly as \( x \) increases.
- **\( a = 1 \)**: This is a line with a slope of 1, meaning for every 1 unit increase in \( x \), \( f(x) \) increases by 1. The line will have a 45-degree angle.
- **\( a = 8 \)**: This represents a much steeper line, where the function increases 8 units for every unit increase in \( x \).

### Graphing instructions:
1. For \( a = \frac{1}{8} \), plot points for small values of \( x \), and the slope will be relatively flat.
2. For \( a = 1 \), plot points and draw the diagonal 45-degree line.
3. For \( a = 8 \), draw a steep line, which rises very quickly.

Would you like further details on how to input these into the graphing tool, or have any specific questions on graphing?

Here are five related questions to explore:
1. What happens to the graph as \( a \) gets smaller (e.g., \( a = \frac{1}{100} \))?
2. How would the graph change if \( a \) were negative?
3. What is the difference between the graphs of \( f(x) = ax \) and \( f(x) = ax + b \)?
4. How does changing the value of \( a \) affect the x- and y-intercepts of the graph?
5. What is the significance of the slope in real-world applications of linear functions?

**Tip**: When graphing lines, the slope determines how steep or flat the line will be, and higher values of \( a \) will result in steeper lines.

Graph f(x) = ax for a = 1/8, a = 1, and a = 8, all on the same set of axes.

Learn how to graph the linear function f(x) = ax for a = 1/8, a = 1, and a = 8. This tutorial explains the concept of slope and how different values of a affect the steepness of the graph. Suitable for high school precalculus students.

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