1. The problem involves identifying the equation of a straight line passing through points (-6, 6) and (6, -6). 2. The formula for the slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Calculate the slope: $$m = \frac{-6 - 6}{6 - (-6)} = \frac{-12}{12} = -1$$ 4. Use the point-slope form of the line equation: $$y - y_1 = m(x - x_1)$$ Using point $(-6, 6)$: $$y - 6 = -1(x + 6)$$ 5. Simplify the equation: $$y - 6 = -x - 6$$ $$y = -x - 6 + 6$$ $$y = -x$$ 6. The equation of the line is: $$y = -x$$ This matches the graph description of a line with negative slope passing through (-6,6) and (6,-6).