1. **State the problem:** Find the equation of the line passing through the points $(-4, -4)$ and $(6, 2)$.\n\n2. **Formula used:** The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.\n\n3. **Calculate the slope $m$:**\n$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-4)}{6 - (-4)} = \frac{2 + 4}{6 + 4} = \frac{6}{10} = \frac{\cancel{6}}{\cancel{10}} = \frac{3}{5}$$\n\n4. **Use point-slope form to find $b$:**\nUsing point $(-4, -4)$, substitute into $y = mx + b$:\n$$-4 = \frac{3}{5} \times (-4) + b$$\n$$-4 = -\frac{12}{5} + b$$\nAdd $\frac{12}{5}$ to both sides:\n$$-4 + \frac{12}{5} = b$$\nConvert $-4$ to $\frac{-20}{5}$ to add fractions:\n$$\frac{-20}{5} + \frac{12}{5} = b$$\n$$\frac{-20 + 12}{5} = b$$\n$$\frac{-8}{5} = b$$\n\n5. **Write the final equation:**\n$$y = \frac{3}{5}x - \frac{8}{5}$$\n\nThis is the equation of the line passing through the points $(-4, -4)$ and $(6, 2)$.