1. **State the problem:** Find the equation of the line passing through the points $(-2,6)$ and $(1,-3)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}.$$\n\n3. **Calculate the slope:** Substitute the points into the formula: $$m=\frac{-3 - 6}{1 - (-2)}=\frac{-9}{1+2}=\frac{-9}{3}.$$\n\n4. **Simplify the slope:** $$m=\cancel{\frac{-9}{3}}= -3.$$\n\n5. **Use point-slope form:** The equation of a line with slope $m$ passing through $(x_1,y_1)$ is $$y - y_1 = m(x - x_1).$$\n\n6. **Substitute slope and one point:** Using point $(-2,6)$, $$y - 6 = -3(x - (-2)) = -3(x + 2).$$\n\n7. **Expand and simplify:** $$y - 6 = -3x - 6,$$ then add 6 to both sides: $$y = -3x - 6 + 6 = -3x.$$\n\n**Final answer:** $$\boxed{y = -3x}.$$