1. **State the problem:** Determine if the line given by the equation $4x - 5y = -25$ is perpendicular to the line $y = -\frac{4}{5}x + 2$. 2. **Rewrite the first line in slope-intercept form:** We want to express $4x - 5y = -25$ as $y = mx + b$ where $m$ is the slope. $$4x - 5y = -25$$ Subtract $4x$ from both sides: $$-5y = -4x - 25$$ Divide both sides by $-5$: $$y = \frac{-4x - 25}{-5} = \frac{\cancel{-4}x + \cancel{25}}{\cancel{-5}}$$ More explicitly: $$y = \frac{-4}{-5}x + \frac{-25}{-5} = \frac{4}{5}x + 5$$ 3. **Identify the slope of the first line:** The slope $m_1 = \frac{4}{5}$. 4. **Identify the slope of the second line:** From $y = -\frac{4}{5}x + 2$, the slope $m_2 = -\frac{4}{5}$. 5. **Check if the lines are perpendicular:** Two lines are perpendicular if the product of their slopes is $-1$. Calculate: $$m_1 \times m_2 = \frac{4}{5} \times \left(-\frac{4}{5}\right) = -\frac{16}{25}$$ Since $-\frac{16}{25} \neq -1$, the lines are **not** perpendicular. **Final answer:** The lines are not perpendicular because the product of their slopes is $-\frac{16}{25}$, not $-1$.