The equation of the line is given as:

$y = \frac{1}{3}x - 6$

This is in slope-intercept form, $y = mx + b$, where:

• $m = \frac{1}{3}$ is the slope of the line, meaning for every 3 units moved horizontally, the line goes up by 1 unit.
• $b = -6$ is the y-intercept, meaning the line crosses the y-axis at $y = -6$.

Steps to graph:

1. Start at the y-intercept: The point $(0, -6)$.
2. Use the slope: The slope is $\frac{1}{3}$. From the point $(0, -6)$:
   • Move 3 units to the right (positive x-direction).
   • Move 1 unit up (positive y-direction). This gives the second point $(3, -5)$.
3. Plot both points: $(0, -6)$ and $(3, -5)$.
4. Draw the line: Connect the two points with a straight line.

Now that I've explained the process, would you like me to show the plotted line or do you have any questions?

Here are 5 related questions to deepen understanding:

1. What does a slope of 0 mean for a line?
2. How does changing the slope to a larger positive number affect the line?
3. What happens to the line if the y-intercept becomes positive?
4. How would you graph the line if the slope was negative, say $-\frac{1}{3}$?
5. Can you convert this equation into a standard form?

Tip: Remember that the slope determines the steepness and direction of the line!