1. **State the problem:** Find the intersection point of the two lines given by the equations: $$y = -\frac{1}{2}x - 2$$ and $$y = \frac{1}{4}x + 3$$ 2. **Formula and approach:** To find the intersection, set the two expressions for $y$ equal to each other because at the intersection point both lines have the same $x$ and $y$ values. $$-\frac{1}{2}x - 2 = \frac{1}{4}x + 3$$ 3. **Solve for $x$:** Move all $x$ terms to one side and constants to the other: $$-\frac{1}{2}x - \frac{1}{4}x = 3 + 2$$ Combine like terms: $$-\frac{1}{2}x - \frac{1}{4}x = -\frac{2}{4}x - \frac{1}{4}x = -\frac{3}{4}x$$ So: $$-\frac{3}{4}x = 5$$ Divide both sides by $-\frac{3}{4}$: $$x = \frac{5}{-\frac{3}{4}} = 5 \times \cancel{\frac{4}{3}} = -\frac{20}{3}$$ 4. **Find $y$ by substituting $x$ back into one of the original equations:** Using $$y = \frac{1}{4}x + 3$$: $$y = \frac{1}{4} \times \left(-\frac{20}{3}\right) + 3 = -\frac{20}{12} + 3 = -\frac{5}{3} + 3$$ Convert 3 to thirds: $$3 = \frac{9}{3}$$ So: $$y = -\frac{5}{3} + \frac{9}{3} = \frac{4}{3}$$ 5. **Final answer:** The lines intersect at $$\left(-\frac{20}{3}, \frac{4}{3}\right)$$