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.