1. **State the problem:** Find the equation of the line given by the point-slope form: $$y + 3 = \frac{1}{2}(x - 4)$$ 2. **Recall the point-slope form formula:** $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Identify the slope and point:** From the equation, slope $m = \frac{1}{2}$ and point $(x_1, y_1) = (4, -3)$. 4. **Convert to slope-intercept form $y = mx + b$:** Start with $$y + 3 = \frac{1}{2}(x - 4)$$ 5. **Distribute the slope:** $$y + 3 = \frac{1}{2}x - \frac{1}{2} \times 4$$ $$y + 3 = \frac{1}{2}x - 2$$ 6. **Isolate $y$ by subtracting 3 from both sides:** $$y + 3 - 3 = \frac{1}{2}x - 2 - 3$$ $$y = \frac{1}{2}x - 5$$ 7. **Final answer:** The equation of the line in slope-intercept form is $$y = \frac{1}{2}x - 5$$ This means the line has slope $\frac{1}{2}$ and crosses the y-axis at $-5$.