To solve this problem, let's first analyze the given equation $y = -2x - 2$.

Step 1: Identify the key features of the equation.

This is a linear equation in slope-intercept form $y = mx + b$, where:

• $m = -2$ (the slope)
• $b = -2$ (the y-intercept)

Step 2: Plot key points.

1. Y-intercept: The graph crosses the y-axis at $(0, -2)$.
2. Slope: The slope is $-2$, which means for every 1 unit you move to the right along the x-axis, the graph moves 2 units down. From the y-intercept $(0, -2)$, if you go 1 unit right, you will move to $(1, -4)$.

Step 3: Match the Graphs.

Now, let's look at the four options:

• Graph A: The line is sloped negatively and passes through $(0, -2)$, but the slope does not match $-2$.
• Graph B: The line passes through $(0, -2)$ and has a slope of $-2$, making it the correct graph.
• Graph C: The slope and intercept do not match.
• Graph D: The slope is wrong for this graph.

Conclusion:

The correct graph is Graph B.

Would you like more details on this solution, or do you have further questions?

Here are 5 relative questions to expand your understanding:

1. How do you calculate the slope of a line given two points?
2. What is the significance of the y-intercept in a linear equation?
3. How would the graph change if the slope was positive instead of negative?
4. How do you graph an equation if it’s given in standard form $Ax + By = C$?
5. What are the steps to convert from point-slope form to slope-intercept form?

Tip: When graphing linear equations, always start by plotting the y-intercept and then use the slope to find other points.