To determine which graph corresponds to the equation $y = -0.5x - 3$, let us break down the key characteristics of the equation:

1. Slope: The slope ($m$) is $-0.5$. This means the line slopes downward as $x$ increases, at a rate of $-0.5$ (for every 1 unit increase in $x$, $y$ decreases by 0.5).

2. Y-intercept: The $y$-intercept ($b$) is $-3$. This is the point where the line crosses the $y$-axis, at $(0, -3)$.

Analyze Each Graph:

• The first graph has a negative slope and crosses the $y$-axis at $(0, -3)$. This matches the equation $y = -0.5x - 3$.
• The second graph has a positive slope, which does not match the negative slope of $-0.5$.
• The third graph has a positive slope as well, which again does not match the given equation.

Conclusion:

The first graph is the correct representation of the equation $y = -0.5x - 3$.

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Questions to expand learning:

1. What are the steps to graph a linear equation manually?
2. How do changes in the slope affect the steepness of a line?
3. Why is the y-intercept important in identifying a graph?
4. How would the graph change if the slope was positive?
5. What are the characteristics of a vertical or horizontal line?

Tip: When analyzing graphs, always check the slope and y-intercept first—they provide quick hints about the correct representation.