1. **State the problem:** Solve the system of equations graphically: $$y = \frac{5}{2}x - 8$$ $$x + 2y = -4$$ 2. **Rewrite the second equation in slope-intercept form:** Start with $$x + 2y = -4$$ Subtract $$x$$ from both sides: $$2y = -x - 4$$ Divide both sides by 2: $$y = -\frac{1}{2}x - 2$$ 3. **Plot both lines:** - First line: $$y = \frac{5}{2}x - 8$$ has slope $$\frac{5}{2}$$ and y-intercept $$-8$$. - Second line: $$y = -\frac{1}{2}x - 2$$ has slope $$-\frac{1}{2}$$ and y-intercept $$-2$$. 4. **Find the intersection point algebraically to confirm the graphical solution:** Set the two expressions for $$y$$ equal: $$\frac{5}{2}x - 8 = -\frac{1}{2}x - 2$$ Add $$\frac{1}{2}x$$ to both sides: $$\frac{5}{2}x + \frac{1}{2}x - 8 = -2$$ Combine like terms: $$3x - 8 = -2$$ Add 8 to both sides: $$3x = 6$$ Divide both sides by 3: $$x = 2$$ Substitute $$x=2$$ into one of the equations to find $$y$$: $$y = \frac{5}{2} \times 2 - 8 = 5 - 8 = -3$$ 5. **Conclusion:** The lines intersect at the point $$(2, -3)$$, which is the solution to the system. This means the graphical solution is the point where the two lines cross at $$(2, -3)$$.