Problem
Line $L_{1}$ has equation $y=3 x+5$ Line $L_{2}$ has equation $6 y+2 x=1$ Show that $L_{1}$ is perpendicular to $L_{2}$. input note: find the gradients of $L_{1}$ and $L_{2}$ (2 marks) $m_{L 1}=$ $m_{L 2}=$
Solution
Step 1 ：Find the gradients of the lines: $m_{L_1} = 3$, $m_{L_2} = -\frac{1}{3}$
Step 2 ：Check if their product is -1: $m_{L_1} \times m_{L_2} = 3 \times -\frac{1}{3} = -1$
Step 3 ：\boxed{\text{The lines } L_1 \text{ and } L_2 \text{ are perpendicular.}}
