https://file.aiquickdraw.com/mathbot/file/17296405984051tucew5m.jpg

The given equation is:

\[
y = -\frac{1}{3}x - 2
\]

This is a **linear equation** in slope-intercept form:  
\[
y = mx + b
\]
where:
- \(m = -\frac{1}{3}\) is the slope of the line.
- \(b = -2\) is the y-intercept (the point where the line crosses the y-axis).

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### Steps to Graph the Equation:

1. **Plot the y-intercept (\(b\))**:
   - When \(x = 0\), \(y = -2\).  
     So, the line passes through the point \((0, -2)\).

2. **Use the slope \(m = -\frac{1}{3}\)**:
   - The slope means for every **1 unit increase in \(x\)**, \(y\) decreases by \(\frac{1}{3}\).
   - Alternatively, move **down 1 unit** on the y-axis for every **3 units right** on the x-axis.

3. **Plot additional points using the slope**:
   - From \((0, -2)\), move **3 units right** to \(x = 3\), and **1 unit down** to \(y = -3\).  
     So, the point \((3, -3)\) lies on the line.
   - Similarly, you could move **left 3 units** and **up 1 unit** from \((0, -2)\), giving the point \((-3, -1)\).

4. **Draw the line through the points**:
   - Connect the points \((0, -2)\), \((3, -3)\), and \((-3, -1)\) with a straight line. The line will extend in both directions.

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Would you like me to help draw the graph or confirm the line's behavior further? 

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### Related Questions:
1. What does a negative slope indicate about a line?
2. How do you find the x-intercept of a line?
3. How would the graph change if the slope were positive?
4. What does changing the y-intercept do to the graph?
5. How do parallel lines relate to slope?

**Tip:** Remember, slope measures both the steepness and direction of the line!

Learn how to graph the linear equation y = -1/3x - 2. This problem covers key algebraic concepts like slope-intercept form, the slope of a line, and plotting points. Suitable for students in Grades 7-10.

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