1. **State the problem:** Find the equation of the line passing through the points (-6,6), (-1,1), (2,-2), and (6,-6). 2. **Formula used:** The equation of a line in slope-intercept form is $$y = mx + c$$ where $m$ is the slope and $c$ is the y-intercept. 3. **Calculate the slope $m$:** Use any two points, for example, (-6,6) and (-1,1). $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 6}{-1 - (-6)} = \frac{-5}{5} = -1$$ 4. **Find the y-intercept $c$:** Use the slope and one point, say (-6,6), in the equation $y = mx + c$. $$6 = (-1)(-6) + c$$ $$6 = 6 + c$$ $$c = 6 - 6 = 0$$ 5. **Write the equation:** Substitute $m = -1$ and $c = 0$ into the slope-intercept form. $$y = -1x + 0$$ $$y = -x$$ 6. **Verify with other points:** Check if (2,-2) satisfies $y = -x$. $$-2 = -(2) = -2$$ (True) Therefore, the equation of the line is $$y = -x$$.