1. **State the problem:** Determine if the line given by the equation $4x + 5y = -30$ is perpendicular to the line given by $y = -\frac{4}{5} + 2$. 2. **Rewrite the second line in slope-intercept form:** The equation $y = -\frac{4}{5} + 2$ is simplified as $y = 2 - \frac{4}{5} = \frac{10}{5} - \frac{4}{5} = \frac{6}{5}$. This is a constant function with slope $0$. 3. **Find the slope of the first line:** Rewrite $4x + 5y = -30$ in slope-intercept form $y = mx + b$. $$4x + 5y = -30$$ $$5y = -4x - 30$$ $$y = \frac{-4x - 30}{5}$$ $$y = -\frac{4}{5}x - 6$$ So, the slope of the first line is $m_1 = -\frac{4}{5}$. 4. **Recall the rule for perpendicular slopes:** Two lines are perpendicular if the product of their slopes is $-1$. 5. **Calculate the product of slopes:** $$m_1 \times m_2 = -\frac{4}{5} \times 0 = 0$$ 6. **Conclusion:** Since the product of slopes is $0$ and not $-1$, the lines are not perpendicular. In fact, the second line is horizontal (slope $0$), and the first line has slope $-\frac{4}{5}$, so they are not perpendicular.