Question

The slope of the line perpendicular to $x-\frac{y}{2}+3=0$ is _____. (2 marks)

Answer 1

Given equation:
$x-\frac{y}{2}+3=0$

$\Rightarrow \frac{-y}{2}=-x-3$

$\Rightarrow y=2x+6$

Comparing the above equation with the slope intercept form of line $y=m_{1}x+c$, where, m is slope of the line.
$\Rightarrow Slope=m_1=2$ (1 mark)

We know that, if $m_1$ and $m_2$ are the slopes of any two lines which are perpendicular, then
$m_1{m}_2=-12\left(m_2\right)=-1m_2=\frac{-1}{2}$

$\therefore$ Slope of the line perpendicular to the given line is $\frac{-1}{2}.$ (1 mark)