1. **State the problem:** Find the equation of a line parallel to the line given by $$y = \frac{3}{4}x - 4$$ that passes through the point $(-2, -5)$. 2. **Recall the rule for parallel lines:** Parallel lines have the same slope. The slope of the given line is $$m = \frac{3}{4}$$. 3. **Use the point-slope form of a line:** The formula is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. Here, $x_1 = -2$ and $y_1 = -5$. 4. **Substitute the values:** $$y - (-5) = \frac{3}{4}(x - (-2))$$ which simplifies to $$y + 5 = \frac{3}{4}(x + 2)$$ 5. **Distribute the slope:** $$y + 5 = \frac{3}{4}x + \frac{3}{4} \times 2 = \frac{3}{4}x + \frac{3}{2}$$ 6. **Isolate $y$ to get slope-intercept form:** $$y = \frac{3}{4}x + \frac{3}{2} - 5$$ 7. **Simplify the constant term:** $$y = \frac{3}{4}x + \frac{3}{2} - \frac{10}{2} = \frac{3}{4}x - \frac{7}{2}$$ **Final answer:** $$\boxed{y = \frac{3}{4}x - \frac{7}{2}}$$