1. **State the problem:** We need to find the equation of the line passing through the points $(-7,6)$ and $(7,-6)$. 2. **Formula used:** The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 6}{7 - (-7)} = \frac{-12}{14} = \frac{\cancel{-12}}{\cancel{14}} = -\frac{6}{7}$$ 4. **Find the y-intercept $b$:** Use point-slope form with point $(-7,6)$: $$6 = -\frac{6}{7} \times (-7) + b$$ $$6 = 6 + b$$ $$b = 6 - 6 = 0$$ 5. **Write the equation:** $$y = -\frac{6}{7}x + 0$$ or simply $$y = -\frac{6}{7}x$$ **Final answer:** The equation of the line is $y = -\frac{6}{7}x$.