1. The problem is to find the equation of the line passing through the points $(-1, 2)$ and $(3, 4)$. 2. The formula to find the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the given points into the slope formula: $$m = \frac{4 - 2}{3 - (-1)} = \frac{2}{3 + 1} = \frac{2}{4}$$ 4. Simplify the fraction: $$m = \frac{\cancel{2}}{\cancel{4}} = \frac{1}{2}$$ 5. Use the point-slope form of the line equation: $$y - y_1 = m(x - x_1)$$ 6. Substitute $m = \frac{1}{2}$ and point $(-1, 2)$: $$y - 2 = \frac{1}{2}(x - (-1)) = \frac{1}{2}(x + 1)$$ 7. Distribute the slope on the right side: $$y - 2 = \frac{1}{2}x + \frac{1}{2}$$ 8. Add 2 to both sides to solve for $y$: $$y = \frac{1}{2}x + \frac{1}{2} + 2$$ 9. Convert 2 to a fraction with denominator 2 to add: $$y = \frac{1}{2}x + \frac{1}{2} + \frac{4}{2}$$ 10. Add the fractions: $$y = \frac{1}{2}x + \frac{5}{2}$$ The equation of the line passing through the points $(-1, 2)$ and $(3, 4)$ is $$y = \frac{1}{2}x + \frac{5}{2}$$.