Graph Identification 8C0Abc

1. **State the problem:** We need to identify which graph corresponds to the equation $$9x + 2y = 9$$. 2. **Rewrite the equation in slope-intercept form:** To understand the graph, solve for $y$: $$9x + 2y = 9$$ Subtract $9x$ from both sides: $$2y = 9 - 9x$$ Divide both sides by 2: $$y = \frac{9 - 9x}{2} = \frac{9}{2} - \frac{9}{2}x$$ 3. **Interpret the slope and intercepts:** - The slope is $$-\frac{9}{2} = -4.5$$, which is a steep negative slope. - The y-intercept is $$\frac{9}{2} = 4.5$$. 4. **Find the x-intercept:** Set $y=0$: $$0 = \frac{9}{2} - \frac{9}{2}x$$ $$\frac{9}{2}x = \frac{9}{2}$$ $$x = \frac{\frac{9}{2}}{\frac{9}{2}} = 1$$ 5. **Match with the graphs:** - The line crosses the y-axis at 4.5 and the x-axis at 1. - The slope is steep and negative. - According to the descriptions: - Graph D is a steep negative-slope line crossing the y-axis near 4.5 and the x-axis near 1. 6. **Conclusion:** The graph representing the equation $$9x + 2y = 9$$ is **Graph D**.