1. **State the problem:** Find the equation of the line with slope $\frac{1}{2}$ passing through the point $(2, 3)$. 2. **Formula used:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Substitute the given values:** $$y - 3 = \frac{1}{2}(x - 2)$$ 4. **Simplify the equation:** $$y - 3 = \frac{1}{2}x - 1$$ 5. **Solve for $y$ to get slope-intercept form:** $$y = \frac{1}{2}x - 1 + 3$$ $$y = \frac{1}{2}x + 2$$ 6. **Interpretation:** The equation of the line is $y = \frac{1}{2}x + 2$. 7. **Check options:** This matches option b. **Final answer:** $y = \frac{1}{2}x + 2$ (option b).