Perpendicular Slope 98396B

1. **State the problem:** We need to find the slope of a line perpendicular to the line given by the equation $$4x - 6y = -60$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$, where $$m$$ is the slope. Start with the given equation: $$4x - 6y = -60$$ Subtract $$4x$$ from both sides: $$-6y = -4x - 60$$ Divide both sides by $$-6$$: $$y = \frac{-4x - 60}{-6}$$ Simplify the fraction: $$y = \frac{-4x}{-6} + \frac{-60}{-6} = \frac{4}{6}x + 10$$ 3. **Simplify the slope:** $$m = \frac{4}{6} = \frac{2}{3}$$ 4. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. So, $$m_{\perp} = -\frac{1}{m} = -\frac{1}{\frac{2}{3}} = -\frac{3}{2}$$ 5. **Final answer:** The slope of the line perpendicular to the given line is $$-\frac{3}{2}$$.