1. **State the problem:** Find the equation of the line passing through points $(2,5)$ and $(5,-1)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line in point-slope form is $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope:** $$m=\frac{-1 - 5}{5 - 2} = \frac{-6}{3} = -2$$ 4. **Write the equation using point $(2,5)$:** $$y - 5 = -2(x - 2)$$ 5. **Simplify the equation:** $$y - 5 = -2x + 4$$ $$y = -2x + 4 + 5$$ $$y = -2x + 9$$ 6. **Final answer:** The equation of the line is $$y = -2x + 9$$