This question requires applying the point-slope form of a line. From the textbook, the point-slope form states that for a line with slope m passing through point $(x_0, y_0)$, the equation is $y - y_0 = m(x - x_0)$. Here, the given point is $(-4, 3)$ and slope $m = \frac{1}{2}$. Substituting these values gives $y - 3 = \frac{1}{2}(x - (-4))$, which simplifies to $y - 3 = \frac{1}{2}(x + 4)$.