1. **State the problem:** Find the equation of the line passing through points (0, 4) and (4, 2) in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ is given by $$m=\frac{y_2-y_1}{x_2-x_1}$$ where $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(4,2)$. 3. **Calculate the slope:** $$m=\frac{2-4}{4-0}=\frac{-2}{4}$$ 4. **Simplify the slope:** $$m=\frac{\cancel{-2}}{\cancel{4}}=-\frac{1}{2}$$ 5. **Use slope-intercept form:** $$y=mx+b$$ 6. **Substitute slope and point (0,4) to find $b$:** $$4=-\frac{1}{2}\times 0 + b$$ 7. **Simplify to find $b$:** $$4=b$$ 8. **Write the final equation:** $$y=-\frac{1}{2}x+4$$ This is the fully simplified slope-intercept form of the line.