https://file.aiquickdraw.com/mathbot/file/1726082242622n5wbwlit.jpg

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!

Learn how to graph the linear equation y = (1/3)x - 6. This problem covers the slope-intercept form and graphing key concepts. Suitable for students in Grades 7-9, it explains how to plot points using the slope and intercept.

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