1. **State the problem:** Find the equation of the line perpendicular to the given line passing through the point $(3,4)$. 2. **Identify the slope of the given line:** The line passes through points $(-3,2)$ and $(0,1)$. Use the slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 2}{0 - (-3)} = \frac{-1}{3} = -\frac{1}{3}$$ 3. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. $$m_{\perp} = -\frac{1}{m} = -\frac{1}{-\frac{1}{3}} = 3$$ 4. **Use point-slope form to find the equation:** The point-slope form is $$y - y_1 = m(x - x_1)$$ Using point $(3,4)$ and slope $3$: $$y - 4 = 3(x - 3)$$ 5. **Simplify the equation:** $$y - 4 = 3x - 9$$ $$y = 3x - 9 + 4$$ $$y = 3x - 5$$ **Final answer:** $$y = 3x - 5$$