1. **State the problem:** We are given two points $(4,0)$ and $(0,2)$ and need to find the equation of the line passing through these points. 2. **Formula used:** The slope-intercept form of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - 4} = \frac{2}{-4} = -\frac{1}{2}$$ 4. **Find the y-intercept $b$:** Use point $(0,2)$ which lies on the y-axis, so $b = 2$. 5. **Write the equation:** $$y = -\frac{1}{2}x + 2$$ 6. **Match with options:** This corresponds to option A: $y = -0.5x + 2$. **Final answer:** $y = -0.5x + 2$