If a line has a slope of \( -4 \), what is the slope of a line that is perpendicular to it?

If a line has a slope of \( -4 \), the slope of a line that is perpendicular to it can be found by taking the negative reciprocal of the original slope. The negative reciprocal of \( -4 \) is \( \frac{1}{4} \). Therefore, the slope of the perpendicular line is \( \frac{1}{4} \). This concept is not only crucial in algebra but also comes in handy in various real-world scenarios, like architecture or engineering design, where creating perpendicular angles is essential for structural stability. Think of it as a dance; when one line leads with a negative slope, its perpendicular partner twirls gracefully into a positive slope!