1. **State the problem:** Find the equation of the line passing through points $(-7,6)$ and $(6,-7)$ in slope-intercept form $y=mx+b$. 2. **Find the slope $m$:** Use the formula $$m=\frac{y_2-y_1}{x_2-x_1}$$ where $(x_1,y_1)=(-7,6)$ and $(x_2,y_2)=(6,-7)$. 3. Calculate the slope: $$m=\frac{-7-6}{6-(-7)}=\frac{-13}{6+7}=\frac{-13}{13}=-1$$ 4. **Use slope-intercept form:** $y=mx+b$. Substitute $m=-1$ and one point, say $(-7,6)$, to find $b$. 5. Substitute: $$6=(-1)(-7)+b$$ $$6=7+b$$ 6. Solve for $b$: $$b=6-7=-1$$ 7. **Write the final equation:** $$y=-1x-1$$ or simply $$y=-x-1$$ This is the fully simplified slope-intercept form of the line.