1. **State the problem:** We need to find the equation of the line passing through the points $(-3, 2)$ and $(1, -6)$ in slope-intercept form, which is $y = mx + b$. 2. **Find the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (-3, 2)$ and $(x_2, y_2) = (1, -6)$. 3. Substitute the values: $$m = \frac{-6 - 2}{1 - (-3)} = \frac{-8}{1 + 3} = \frac{-8}{4}$$ 4. Simplify the fraction: $$m = \frac{\cancel{-8}}{\cancel{4}} = -2$$ 5. **Use the slope-intercept form $y = mx + b$ and plug in one point to find $b$:** Using point $(-3, 2)$, $$2 = -2(-3) + b$$ 6. Simplify: $$2 = 6 + b$$ 7. Solve for $b$: $$b = 2 - 6 = -4$$ 8. **Write the final equation:** $$y = -2x - 4$$ This is the equation of the line in slope-intercept form.