The equation given is $y = -2x - 2$, and you have provided a blank graph to plot it on. Let's break down how to plot this line.

Step-by-Step Guide to Plotting:

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form $y = mx + b$, where:
     • $m = -2$ is the slope (which tells us how steep the line is),
     • $b = -2$ is the y-intercept (which is the point where the line crosses the y-axis).

2. Plot the y-intercept:

   • The y-intercept is $-2$. So, on the graph, locate $(0, -2)$ and mark it.

3. Use the slope to find another point:

   • The slope $m = -2$ can be written as $\frac{-2}{1}$. This means for every 1 unit you move to the right (increasing x by 1), you move 2 units down (decreasing y by 2).
   • Starting from $(0, -2)$, move 1 unit right to $x = 1$ and 2 units down to $y = -4$. So another point on the line is $(1, -4)$.

4. Draw the line:

   • With these two points, $(0, -2)$ and $(1, -4)$, draw a straight line through them. You can also extend the line in both directions to fill the graph.

This will give you the graph of the equation $y = -2x - 2$.

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Related Questions:

1. How do you determine the slope from a linear equation?
2. What does the y-intercept represent in real-world problems?
3. How would the graph change if the slope was positive?
4. What happens to the line if the y-intercept increases?
5. Can you find the x-intercept from the equation?

Tip: When dealing with linear equations, always start by identifying the slope and y-intercept to make plotting easier.