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To determine the correct graph for the function \( f(x) = -x - 2 \), let’s analyze its key properties:

1. **Slope**: The function has a slope of -1, indicating a downward slant from left to right.
2. **Y-intercept**: The y-intercept is -2, which means the graph crosses the y-axis at the point (0, -2).

With these two characteristics, we should look for a graph where:
- The line crosses the y-axis at -2.
- The line slopes downward with a slope of -1, meaning for each step right (1 unit increase in \( x \)), the \( y \) value decreases by 1.

After examining each graph:
- **Graph B** shows a line that crosses the y-axis at -2 and has a downward slope with a slope of -1.

**Answer**: The correct choice is **B**.

Would you like more details or have any questions about this solution?

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Here are 5 related questions that expand on this concept:
1. How do you determine the slope of a line from its equation?
2. What does the y-intercept represent in a linear equation?
3. How would the graph change if the function was \( f(x) = x - 2 \)?
4. How does changing the slope affect the steepness of the line?
5. What would the graph look like for \( f(x) = -x + 2 \)?

**Tip**: For linear functions in the form \( f(x) = mx + b \), \( m \) represents the slope, and \( b \) represents the y-intercept.

Select the correct graph for the function f(x) = -x - 2.

Learn how to identify the correct graph for the linear function f(x) = -x - 2 by analyzing its slope and y-intercept. This solution provides insight into graphing linear equations, finding slopes, and understanding intercepts. Suitable for students in Grades 8-10.

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