1. **Problem Statement:** Verify that two lines are perpendicular by using their slopes. 2. **Formula and Rule:** Two lines are perpendicular if and only if the product of their slopes is $-1$. 3. **Step-by-step Explanation:** - Find the slope of the first line, $m_1$. - Find the slope of the second line, $m_2$. - Calculate the product $m_1 \times m_2$. - If $m_1 \times m_2 = -1$, then the lines are perpendicular. 4. **Example:** Suppose the slopes are $m_1 = 2$ and $m_2 = -\frac{1}{2}$. - Calculate the product: $$2 \times \left(-\frac{1}{2}\right) = -1$$ - Since the product is $-1$, the lines are perpendicular. 5. **Conclusion:** By verifying that the product of the slopes equals $-1$, we confirm the lines are perpendicular.