1. **State the problem:** Find the equation of the line passing through points $(1,2)$ and $(3,-4)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2-y_1}{x_2-x_1}$$ 3. **Calculate the slope:** $$m=\frac{-4-2}{3-1}=\frac{-6}{2}=-3$$ 4. **Use point-slope form:** The equation of a line with slope $m$ passing through $(x_1,y_1)$ is $$y-y_1=m(x-x_1)$$ 5. **Substitute values:** $$y-2=-3(x-1)$$ 6. **Simplify:** $$y-2=-3x+3$$ 7. **Isolate $y$:** $$y=-3x+3+2$$ $$y=-3x+5$$ **Final answer:** The equation of the line is $$y=-3x+5$$