1. **State the problem:** We need to graph the system of linear inequalities: $$y < -3x + 3$$ $$y > x - \frac{3}{2}$$ 2. **Understand the inequalities:** - The first inequality $y < -3x + 3$ means the region below the line $y = -3x + 3$. - The second inequality $y > x - \frac{3}{2}$ means the region above the line $y = x - \frac{3}{2}$. 3. **Graph the boundary lines:** - For $y = -3x + 3$, the slope is $-3$ and the y-intercept is $3$. This line is dashed because the inequality is strict ($<$). - For $y = x - \frac{3}{2}$, the slope is $1$ and the y-intercept is $-\frac{3}{2}$. This line is also dashed because the inequality is strict ($>$). 4. **Determine the solution region:** - The solution to the system is the set of points that satisfy both inequalities simultaneously. - This means the region below the blue dashed line ($y < -3x + 3$) and above the red dashed line ($y > x - \frac{3}{2}$). 5. **Interpret the graphs described:** - The first graph shows the blue dashed line with slope $-3$ and the red dashed line with slope $1$. - The shaded region is above the red line and below the blue line, which matches our solution. **Final answer:** The correct graph is the first one, where the shaded region lies between the two dashed lines, above $y = x - \frac{3}{2}$ and below $y = -3x + 3$.