1. **State the problem:** Solve the system of linear equations by graphing: $$4x - 2y = 8$$ $$y = \frac{3}{2}x - 2$$ 2. **Rewrite the first equation in slope-intercept form $y = mx + b$:** Start with: $$4x - 2y = 8$$ Subtract $4x$ from both sides: $$-2y = -4x + 8$$ Divide both sides by $-2$: $$y = \frac{\cancel{-4}x}{\cancel{-2}} - \frac{8}{-2} = 2x - 4$$ 3. **Now we have two equations in slope-intercept form:** $$y = 2x - 4$$ $$y = \frac{3}{2}x - 2$$ 4. **Find the intersection point by setting the right sides equal:** $$2x - 4 = \frac{3}{2}x - 2$$ Subtract $\frac{3}{2}x$ from both sides: $$2x - \frac{3}{2}x - 4 = -2$$ Rewrite $2x$ as $\frac{4}{2}x$: $$\frac{4}{2}x - \frac{3}{2}x - 4 = -2$$ Simplify: $$\frac{1}{2}x - 4 = -2$$ Add $4$ to both sides: $$\frac{1}{2}x = 2$$ Multiply both sides by $2$: $$x = 4$$ 5. **Substitute $x=4$ into one of the equations to find $y$:** Using $y = 2x - 4$: $$y = 2(4) - 4 = 8 - 4 = 4$$ 6. **Solution:** The lines intersect at the point $\boxed{(4, 4)}$. 7. **Interpretation:** This means the solution to the system is $x=4$ and $y=4$.