https://file.aiquickdraw.com/mathbot/file/1726685443608z35dpqjy.jpg

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.

On a piece of paper, graph y = -2x - 2. Then determine which answer choice matches the graph you drew.

Learn how to graph the linear equation y = -2x - 2 and match it with the correct graph. This problem focuses on slope-intercept form and graphing techniques suitable for students in Grades 7-9.

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