Q. 9

The lines $y = 2 x - 1$ and $y = a x + 2$ are perpendicular if $a =$ ____.

Verified

Answer

The lines $y = 2 x - 1$ and $y = a x + 2$ are perpendicular if $a = - \frac{1}{2}$ .

1Step 1. Given information.

We have two equation:

$y = 2 x - 1 y = a x + 2$

2Step 2. Fill the blank.

Two non-vertical lines are perpendicular if and only if the product of their slopes is $- 1 .$

Comparing the two equation with slope intercept form $y = m x + b$ , we get:

$m_{1} = 2 m_{2} = a$

Since two lines are perpendicular, we get:

$m_{1} \times m_{2} = - 1 2 \times a = - 1 a = - \frac{1}{2}$