1. **State the problem:** Find the equation of the line perpendicular to the given line $3x + 5y = -9$ that passes through the point $(3, 0)$. 2. **Rewrite the given line in slope-intercept form:** $$3x + 5y = -9 \implies 5y = -3x - 9 \implies y = -\frac{3}{5}x - \frac{9}{5}$$ The slope of the given line is $m = -\frac{3}{5}$. 3. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. $$m_{\perp} = -\frac{1}{m} = -\frac{1}{-\frac{3}{5}} = \frac{5}{3}$$ 4. **Use point-slope form to find the equation of the perpendicular line passing through $(3, 0)$:** $$y - y_1 = m_{\perp}(x - x_1)$$ $$y - 0 = \frac{5}{3}(x - 3)$$ $$y = \frac{5}{3}x - 5$$ 5. **Rewrite in standard form:** Multiply both sides by 3: $$3y = 5x - 15$$ Bring all terms to one side: $$5x - 3y = 15$$ 6. **Check the options:** The equation $5x - 3y = 15$ matches one of the given options. **Final answer:** $$5x - 3y = 15$$