1. **State the problem:** Find the equation of the line perpendicular to the line $$y=\frac{1}{3}x$$ and passing through the point $$(2,5)$$. 2. **Recall the rule for perpendicular slopes:** If a line has slope $$m$$, then a line perpendicular to it has slope $$-\frac{1}{m}$$. 3. **Identify the slope of the given line:** The slope of $$y=\frac{1}{3}x$$ is $$m=\frac{1}{3}$$. 4. **Calculate the perpendicular slope:** $$m_{\perp} = -\frac{1}{\frac{1}{3}} = -3$$. 5. **Use point-slope form:** The equation of a line with slope $$m$$ passing through $$(x_1,y_1)$$ is $$y - y_1 = m(x - x_1)$$. 6. **Substitute values:** $$y - 5 = -3(x - 2)$$. 7. **Simplify:** $$y - 5 = -3x + 6$$ $$y = -3x + 6 + 5$$ $$y = -3x + 11$$. **Final answer:** $$y = -3x + 11$$.