1. **State the problem:** We need to graph the system of inequalities: $$y \leq -\frac{1}{3}x + 2$$ $$y > \frac{4}{3}x - 3$$ 2. **Understand the inequalities:** - The first inequality means the region below or on the line $y = -\frac{1}{3}x + 2$. - The second inequality means the region above the line $y = \frac{4}{3}x - 3$, but not including the line itself. 3. **Graph each boundary line:** - For $y = -\frac{1}{3}x + 2$, plot the y-intercept at $(0,2)$ and use the slope $-\frac{1}{3}$ to find another point (e.g., from $(0,2)$ go right 3 units and down 1 unit to $(3,1)$). This line is solid because of the $\leq$ sign. - For $y = \frac{4}{3}x - 3$, plot the y-intercept at $(0,-3)$ and use the slope $\frac{4}{3}$ to find another point (e.g., from $(0,-3)$ go right 3 units and up 4 units to $(3,1)$). This line is dashed because of the $>$ sign. 4. **Shade the solution regions:** - Shade below or on the first line. - Shade above the second line. 5. **Find the intersection region:** - The solution to the system is where the shaded regions overlap. 6. **Summary:** - The graph shows two lines intersecting at $(3,1)$. - The solution region is the area below or on the line $y = -\frac{1}{3}x + 2$ and above the line $y = \frac{4}{3}x - 3$. This completes the graphing of the system of inequalities.