1. The problem is to transpose the equation $$2x + 4y = 8$$ into slope-intercept form, which is $$y = mx + c$$ where $$m$$ is the slope and $$c$$ is the y-intercept. 2. Start with the given equation: $$2x + 4y = 8$$ 3. To isolate $$y$$, subtract $$2x$$ from both sides: $$4y = -2x + 8$$ 4. Now divide every term by 4 to solve for $$y$$: $$y = \frac{-2x}{4} + \frac{8}{4}$$ 5. Simplify the fractions: $$y = -\frac{1}{2}x + 2$$ 6. This is the slope-intercept form where the slope $$m = -\frac{1}{2}$$ and the y-intercept $$c = 2$$. 7. Comparing with the options given, the correct answer is: $$y = -\frac{1}{2}x + 2$$