Thank you for reporting, we will resolve it shortly
Q.
Find the equation of a line perpendicular to the line $x - 2y + 3 = 0$ and passing through the point $(1,-2)$.
Straight Lines
Solution:
Given line $x - 2y + 3 = 0$ can be written as
$y=\frac{1}{2}x+\frac{3}{2} \quad\ldots\left(i\right)$
Slope of the line $\left(i\right)$ is $m_{1}=\frac{1}{2}$. Therefore, slope of the line perpendicular to line $\left(i\right)$ is
$m_{2}=-\frac{1}{m_{1}}=-2$
$\therefore $ Equation of the line with slope $-2$ and passing through the point $\left(1, -2\right)$ is
$y-\left(-2\right)=-2\left(x-1\right)$ or $y=-2x$