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)
$m_{L 1}=$
$m_{L 2}=$

Answer

Expert–verified

Hide Steps

Answer

\boxed{\text{The lines } L_1 \text{ and } L_2 \text{ are perpendicular.}}

Steps

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.}}