To graph the line represented by the equation $y = \frac{1}{3}x - 6$, follow these steps:

1. Identify the y-intercept: The equation is already in slope-intercept form $y = mx + b$, where $m = \frac{1}{3}$ is the slope, and $b = -6$ is the y-intercept. So, the line crosses the y-axis at $(0, -6)$.

2. Plot the y-intercept: On the graph, mark the point where $y = -6$ (i.e., at the coordinates $(0, -6)$).

3. Use the slope to find another point: The slope is $\frac{1}{3}$, meaning for every 3 units you move horizontally (right), you move 1 unit vertically (up). From the point $(0, -6)$, move 3 units to the right to $x = 3$, and then move 1 unit up to $y = -5$. The new point is $(3, -5)$.

4. Draw the line: Once you have at least two points, draw a straight line through them, and extend it across the graph.

Would you like more details on how to plot this graph, or any other mathematical questions? Here are some related topics:

1. How to calculate the slope and y-intercept from an equation.
2. How to graph a line using two points.
3. What is the meaning of slope in real-life contexts?
4. How does changing the slope affect the graph of a line?
5. What is the significance of the y-intercept?

Tip: The slope of a line tells you how steep it is. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.