1. **State the problem:** Find the equation of the line passing through points $(3, -4)$ and $(-2, 6)$ in gradient-intercept form $y = mx + b$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** $$m = \frac{6 - (-4)}{-2 - 3} = \frac{6 + 4}{-5} = \frac{10}{-5} = -2$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Using point $(3, -4)$: $$y - (-4) = -2(x - 3)$$ $$y + 4 = -2x + 6$$ 5. **Convert to gradient-intercept form:** $$y = -2x + 6 - 4$$ $$y = -2x + 2$$ **Final answer:** The equation of the line is $$y = -2x + 2$$