1. Let's state the problem: We want to know if the slope of a line perpendicular to another line is always the negative inverse of the original line's slope. 2. The formula for the slope of a line perpendicular to another line with slope $m$ is $m_{\perp} = -\frac{1}{m}$. 3. Important rule: Two lines are perpendicular if and only if the product of their slopes is $-1$, i.e., $m \times m_{\perp} = -1$. 4. To verify, suppose the original line has slope $m$. Then the perpendicular slope is $m_{\perp} = -\frac{1}{m}$. 5. Check the product: $$m \times m_{\perp} = m \times \left(-\frac{1}{m}\right) = \cancel{m} \times \left(-\frac{1}{\cancel{m}}\right) = -1$$ 6. Since the product is $-1$, the slopes are negative reciprocals, confirming the rule. 7. Note: This applies only when $m \neq 0$ and $m$ is defined (not vertical lines). Final answer: Yes, the slope of a line perpendicular to another is always the negative inverse of the original line's slope.