1. **State the problem:** We need to graph the inequality $$5x + 4y > -8$$ on the Cartesian plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, first express the inequality as $$y > mx + b$$. Start with: $$5x + 4y > -8$$ Subtract $$5x$$ from both sides: $$4y > -5x - 8$$ Divide both sides by 4: $$y > \frac{-5x - 8}{4}$$ Show cancellation: $$y > \frac{\cancel{4}(-5x - 8)}{\cancel{4}}$$ Simplify: $$y > -\frac{5}{4}x - 2$$ 3. **Interpret the inequality:** The boundary line is $$y = -\frac{5}{4}x - 2$$. Since the inequality is strict (greater than, not greater than or equal to), the boundary line will be dashed. 4. **Graph the boundary line:** Plot the y-intercept at $$-2$$ on the y-axis. Use the slope $$-\frac{5}{4}$$ to find another point: from the y-intercept, go down 5 units and right 4 units. 5. **Shade the solution region:** Since the inequality is $$y > -\frac{5}{4}x - 2$$, shade the region above the dashed line. 6. **Summary:** The graph is a dashed line with equation $$y = -\frac{5}{4}x - 2$$ and the area above this line is shaded to represent all points satisfying $$5x + 4y > -8$$.