1. **Problem:** Write the equation of the line passing through point $(3,5)$ with slope $m=2$. 2. **Formula:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute values:** $$y - 5 = 2(x - 3)$$ 4. **Simplify:** $$y - 5 = 2x - 6$$ 5. **Isolate $y$:** $$y = 2x - 6 + 5$$ $$y = 2x - 1$$ **Final answer:** $$y = 2x - 1$$ This is the equation of the line passing through $(3,5)$ with slope $2$.