The given expression is \( 6x - \frac{1}{3}x \). Let's simplify this linear function:

\[
6x - \frac{1}{3}x = \left(6 - \frac{1}{3}\right)x = \frac{18}{3}x - \frac{1}{3}x = \frac{17}{3}x
\]

So, the simplified linear function is:

\[
y = \frac{17}{3}x
\]

### Characteristics of the linear function:
1. **Slope (m)**: \( \frac{17}{3} \)
2. **y-intercept**: Since there is no constant term, the y-intercept is at \( (0,0) \).

### To graph this function:
- The graph will pass through the origin \( (0, 0) \).
- The slope \( \frac{17}{3} \) means that for every 3 units you move horizontally (to the right), you move 17 units vertically (upwards).

I'll plot the graph of the function.

### Do you want more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the graph change if the slope were negative?
2. What is the effect of adding a constant to the equation?
3. How would you find the x-intercept for any linear equation?
4. Can you find the equation of a line perpendicular to this one?
5. What does the slope tell you about the steepness of the line?

**Tip:** When graphing a linear function, always start by plotting the y-intercept and use the slope to find additional points.

Learn how to simplify and graph the linear function 6x - (1/3)x. This problem covers essential algebra concepts, including slope-intercept form and graphing techniques. Suitable for students in Grades 8-10, the solution demonstrates how to find the slope and y-intercept, and provides a detailed step-by-step graphing guide.

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