1. **State the problem:** We need to identify which graph represents the function given by the equation $$-2x - 5y = -10$$. 2. **Rewrite the equation in slope-intercept form:** To understand the graph, solve for $y$: $$-2x - 5y = -10$$ Add $2x$ to both sides: $$-5y = 2x - 10$$ Divide both sides by $-5$: $$y = \frac{2x - 10}{-5} = \frac{2x}{-5} - \frac{10}{-5} = -\frac{2}{5}x + 2$$ 3. **Interpret the slope and intercept:** - The slope is $-\frac{2}{5}$, which means the line goes downwards as $x$ increases. - The $y$-intercept is $2$, so the line crosses the $y$-axis at $(0, 2)$. 4. **Check the graphs:** - Graph A shows a line with a positive slope and $y$-intercept at $-2$, so it does not match. - Graph C shows a line with a negative slope and $y$-intercept at $2$, which matches our equation. - Graphs B and D are partial and do not show the full line clearly, but B has a positive slope and D has a negative slope but different intercept. 5. **Conclusion:** The graph that represents the function $$-2x - 5y = -10$$ is **Graph C**. **Final answer:** Graph C