1. **State the problem:** We need to find the graphical representation of the two lines given by the equations: $$-8x + 6y = -22$$ $$-3x + 9y = 12$$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$ to understand their slopes and intercepts:** For the first line: $$-8x + 6y = -22$$ Add $8x$ to both sides: $$6y = 8x - 22$$ Divide both sides by 6: $$y = \frac{8x}{6} - \frac{22}{6}$$ Simplify the fractions: $$y = \frac{4}{3}x - \frac{11}{3}$$ For the second line: $$-3x + 9y = 12$$ Add $3x$ to both sides: $$9y = 3x + 12$$ Divide both sides by 9: $$y = \frac{3x}{9} + \frac{12}{9}$$ Simplify the fractions: $$y = \frac{1}{3}x + \frac{4}{3}$$ 3. **Interpretation:** - The first line has slope $\frac{4}{3}$ and y-intercept $-\frac{11}{3} \approx -3.67$. - The second line has slope $\frac{1}{3}$ and y-intercept $\frac{4}{3} \approx 1.33$. 4. **Check the graphs:** - The correct graph should show two straight lines with positive slopes $\frac{4}{3}$ (steeper) and $\frac{1}{3}$ (less steep). - The first line crosses the y-axis below zero, the second above zero. 5. **Conclusion:** The graph in the top-left position with two lines matching these slopes and intercepts is the correct graphical representation. **Final answer:** The top-left graph correctly represents the two lines.