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 formula and rules:** Lines that are parallel have the same slope. The slope-intercept form of a line is $$y = mx + c$$ where $m$ is the slope and $c$ is the y-intercept. 3. **Identify the slope of the given line:** The slope $m$ of the given line is $$\frac{3}{4}$$. Since the new line is parallel, it will have the same slope $$m = \frac{3}{4}$$. 4. **Use the point-slope form to find $c$:** The new line passes through $(-2, -5)$, so substitute $x = -2$, $y = -5$, and $m = \frac{3}{4}$ into $$y = mx + c$$ to find $c$. $$-5 = \frac{3}{4} \times (-2) + c$$ $$-5 = -\frac{6}{4} + c$$ $$-5 = -\frac{3}{2} + c$$ 5. **Solve for $c$:** $$c = -5 + \frac{3}{2}$$ Convert $-5$ to a fraction with denominator 2: $$-5 = -\frac{10}{2}$$ So, $$c = -\frac{10}{2} + \frac{3}{2} = -\frac{7}{2}$$ 6. **Write the equation of the new line:** $$y = \frac{3}{4}x - \frac{7}{2}$$ **Final answer:** $$y = \frac{3}{4}x - \frac{7}{2}$$