1. **State the problem:** We need to graph the inequality $$-5x + 2y > -8$$ on the Cartesian coordinate system. 2. **Rewrite the inequality in slope-intercept form:** To graph, express $$y$$ in terms of $$x$$. Start with: $$-5x + 2y > -8$$ Add $$5x$$ to both sides: $$\cancel{-5x} + 2y > -8 + 5x$$ $$2y > 5x - 8$$ Divide both sides by 2: $$\frac{2y}{\cancel{2}} > \frac{5x - 8}{\cancel{2}}$$ $$y > \frac{5}{2}x - 4$$ 3. **Interpret the inequality:** - The boundary line is $$y = \frac{5}{2}x - 4$$. - Since the inequality is strict ($$>$$), the boundary line is dashed. - The solution region is above the line because $$y$$ is greater than the expression. 4. **Graphing steps:** - Plot the boundary line $$y = \frac{5}{2}x - 4$$ as a dashed line. - To plot, find intercepts: - When $$x=0$$, $$y = -4$$. - When $$y=0$$, solve $$0 = \frac{5}{2}x - 4$$: $$\frac{5}{2}x = 4$$ $$x = \frac{4}{\frac{5}{2}} = \frac{4 \times 2}{5} = \frac{8}{5} = 1.6$$ - Shade the region above the line. This completes the graphing of the inequality.