1. **State the problem:** We want to graph the region containing all points $(x,y)$ such that $2x + y < 3$. 2. **Rewrite the inequality:** To graph this, first express $y$ in terms of $x$: $$y < 3 - 2x$$ 3. **Graph the boundary line:** The boundary line is given by the equation: $$y = 3 - 2x$$ This line divides the plane into two half-planes. 4. **Determine which side to shade:** Since the inequality is $y < 3 - 2x$, we shade the region below the line. 5. **Plot details:** The line $y = 3 - 2x$ has a y-intercept at $(0,3)$ and an x-intercept at $(\frac{3}{2},0)$. 6. **Summary:** The solution set is all points below the line $y = 3 - 2x$, not including the line itself (since the inequality is strict).