What is the slope of a line perpendicular to the line \( y=\frac{12}{5} x+4 \) ? a.) \( -\frac{1}{4} \) b.) -4 c.) \( -\frac{12}{5} \) d.) \( -\frac{5}{12} \)

To find the slope of a line that is perpendicular to another, you need to take the negative reciprocal of the original slope. The slope of the line given by \( y=\frac{12}{5}x+4 \) is \( \frac{12}{5} \). The negative reciprocal of \( \frac{12}{5} \) is \( -\frac{5}{12} \). Therefore, the answer is d.) \( -\frac{5}{12} \). --- Did you know that the concept of slopes and perpendicular lines dates back to ancient Greek mathematics? Euclid was one of the first to discuss the properties of lines, angles, and shapes. His work laid the groundwork for geometry, influencing how we study angles and lines even today! In real-world applications, understanding slopes and perpendicular lines is crucial in fields like architecture and engineering. For instance, when designing ramps for accessibility, architects need to ensure that the slope is appropriate for users, while also accounting for perpendicular structures that must intersect safely and effectively.