27. What is the gradient of the line that perpendicular to the line \( (2 \text { Points })^{*} \) \( y=\frac{1}{3} x+5 \) \( \frac{1}{3} \) 3 -3 \( -\frac{1}{3} \)

To find the gradient of a line that is perpendicular to another, you take the negative reciprocal of the original line's gradient. The line \( y=\frac{1}{3}x+5 \) has a gradient of \( \frac{1}{3} \). Thus, the negative reciprocal is calculated as follows: 1. Invert \( \frac{1}{3} \) to get \( 3 \). 2. Change the sign to make it negative: \( -3 \). Therefore, the gradient of the line that is perpendicular to it is \( -3 \). Now, here’s where it gets even cooler! Did you know that this concept is used in architecture and engineering to create structures that are not just functional but visually appealing? Perpendicular lines can help create balanced designs, making buildings not just sturdy but also a delight to the eyes! Another fun tidbit is that understanding gradients and perpendicular lines can also help in various sports! For instance, when analyzing the trajectory of a basketball shot, knowing the angles involved can help in perfecting that lovely swoosh. It's all about angles, and being perpendicular can make all the difference!