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?

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.