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?

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.