1. **State the problem:** Find the equation of the line passing through the points $(-6, -7)$ and $(6, 7)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}.$$\n\n3. **Calculate the slope:** Substitute the points:\n$$m = \frac{7 - (-7)}{6 - (-6)} = \frac{7 + 7}{6 + 6} = \frac{14}{12}.$$\n\n4. **Simplify the slope:**\n$$m = \frac{\cancel{14}}{\cancel{12}} = \frac{7}{6}.$$\n\n5. **Use point-slope form:** The equation of a line is $$y - y_1 = m(x - x_1).$$ Using point $(-6, -7)$:\n$$y - (-7) = \frac{7}{6}(x - (-6))$$\n$$y + 7 = \frac{7}{6}(x + 6).$$\n\n6. **Expand and simplify:**\n$$y + 7 = \frac{7}{6}x + \frac{7}{6} \times 6 = \frac{7}{6}x + 7.$$\n\n7. **Isolate $y$:**\n$$y = \frac{7}{6}x + 7 - 7 = \frac{7}{6}x.$$\n\n**Final answer:** The equation of the line is $$y = \frac{7}{6}x.$$