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The equation provided is \( y = -3x - 3 \), and you are asked to graph the line.

This is a linear equation in slope-intercept form: \( y = mx + b \), where:
- \( m \) is the slope of the line
- \( b \) is the y-intercept.

For \( y = -3x - 3 \):
- The slope \( m = -3 \), meaning that for every 1 unit increase in \( x \), the value of \( y \) decreases by 3.
- The y-intercept \( b = -3 \), meaning the line crosses the y-axis at \( y = -3 \).

### Steps to graph the line:
1. **Start with the y-intercept:** Plot the point \( (0, -3) \) on the graph. This is where the line crosses the y-axis.
2. **Use the slope:** The slope is \( -3 \), or \( \frac{-3}{1} \). This means you move 1 unit to the right along the x-axis and 3 units down along the y-axis from the y-intercept.
    - From \( (0, -3) \), move right to \( (1, -6) \) and plot this point.
3. **Extend the line:** Continue applying the slope or use another approach (e.g., symmetry or plotting more points) to extend the line in both directions.
4. **Draw the line:** Connect the points to form a straight line.

Would you like me to generate the graph or further explain any of these steps?

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Here are five related questions to deepen your understanding:
1. How does the slope of the line affect its steepness?
2. What is the significance of the y-intercept in a real-world scenario?
3. How would the graph change if the slope were positive?
4. Can you determine the x-intercept for this line?
5. How do parallel and perpendicular lines relate in terms of their slopes?

**Tip:** Always check the sign of the slope to know whether the line will incline upward or downward as you move from left to right.

Learn how to graph the linear equation y = -3x - 3. This problem covers key concepts such as slope and y-intercept, showing how to plot the graph step-by-step. Suitable for students in Grades 6-8.

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