1. The problem is to find the equation of the line passing through the points $(-1, 2)$ and $(3, 4)$. 2. The formula for the slope $m$ of a line 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: $$m = \frac{4 - 2}{3 - (-1)} = \frac{2}{4} = \frac{1}{2}$$ 4. Use the point-slope form of a line equation: $$y - y_1 = m(x - x_1)$$ 5. Substitute $m = \frac{1}{2}$ and point $(-1, 2)$: $$y - 2 = \frac{1}{2}(x - (-1)) = \frac{1}{2}(x + 1)$$ 6. Simplify the equation: $$y - 2 = \frac{1}{2}x + \frac{1}{2}$$ 7. Add 2 to both sides: $$y = \frac{1}{2}x + \frac{1}{2} + 2 = \frac{1}{2}x + \frac{5}{2}$$ The equation of the line is $$y = \frac{1}{2}x + \frac{5}{2}$$.