1. **State the problem:** We need to solve the system of equations by graphing: $$y = \frac{1}{2}x + 1$$ $$y = -x - 2$$ 2. **Understand the method:** The solution to the system is the point where the two lines intersect on the graph. 3. **Graph each line:** - The first line has slope $\frac{1}{2}$ and y-intercept 1. - The second line has slope $-1$ and y-intercept $-2$. 4. **Find the intersection algebraically to confirm:** Set the right sides equal: $$\frac{1}{2}x + 1 = -x - 2$$ 5. **Solve for $x$:** $$\frac{1}{2}x + x = -2 - 1$$ $$\frac{3}{2}x = -3$$ $$x = \frac{-3}{\frac{3}{2}} = -3 \times \frac{2}{3} = -2$$ 6. **Find $y$ by substituting $x = -2$ into one equation:** $$y = \frac{1}{2}(-2) + 1 = -1 + 1 = 0$$ 7. **Conclusion:** The lines intersect at the point $(-2, 0)$. This matches the graphical solution where the two lines cross. **Final answer:** $(-2, 0)$