1. **Problem Statement:** Find the equation of the line passing through the points $(0, 2)$ and $(4, 8)$. 2. **Formula Used:** The slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line in slope-intercept form is: $$y = mx + b$$ where $b$ is the y-intercept. 3. **Calculate the slope:** $$m = \frac{8 - 2}{4 - 0} = \frac{6}{4} = \frac{3}{2}$$ 4. **Find the y-intercept $b$:** Use point $(0, 2)$ which lies on the line: $$2 = \frac{3}{2} \times 0 + b \implies b = 2$$ 5. **Write the equation:** $$y = \frac{3}{2}x + 2$$ 6. **Explanation:** The slope $\frac{3}{2}$ means for every 2 units increase in $x$, $y$ increases by 3 units. The line crosses the y-axis at 2. **Final answer:** $$y = \frac{3}{2}x + 2$$