To determine which graph represents the function $y = -0.5x - 2$, we analyze the following key components of the equation:

1. Slope: The coefficient of $x$, which is $-0.5$, represents the slope of the line. This means the line decreases as $x$ increases.
2. Y-intercept: The constant $-2$ indicates the point where the line intersects the $y$-axis (at $y = -2$).

Step-by-Step Analysis of the Graphs

• Graph A:
  The slope is negative, and the line intersects the $y$-axis below $0$. It appears to have a $y$-intercept of $-2$. This matches our equation.

• Graph B:
  The line has a positive slope, which does not match $-0.5$. Not correct.

• Graph C:
  The line has a negative slope but a positive $y$-intercept (above $0$). Not correct.

• Graph D:
  The line also has a negative slope, but the $y$-intercept is positive $2$. Not correct.

Final Answer:

The correct graph is A.

Do you need further clarification or a breakdown of the solution?
Here are 5 related questions you can explore:

1. What is the general equation of a straight line?
2. How do you determine the slope of a line from its graph?
3. What does a positive vs. negative slope mean for the line's direction?
4. How can you find the $y$-intercept of a line visually?
5. How do you rewrite a line equation in slope-intercept form?

Tip: To verify the slope on a graph, pick two points on the line and use the slope formula $m = \frac{\Delta y}{\Delta x}$.