1. **State the problem:** Find the slope-intercept form of the line passing through the points $(6, 2)$ and $(-3, -7)$. 2. **Formula used:** The slope-intercept form is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - 2}{-3 - 6} = \frac{-9}{-9} = 1$$ 4. **Use point-slope form to find $b$:** Using point $(6, 2)$, $$y = mx + b \Rightarrow 2 = 1 \times 6 + b$$ $$2 = 6 + b$$ $$b = 2 - 6 = -4$$ 5. **Write the slope-intercept form:** $$y = 1x - 4$$ 6. **Final answer:** $$\boxed{y = x - 4}$$