Question

Write the equation of the lines for which $\tan \theta =\frac{1}{2}$, where $\theta$ is the inclination of the line and
$\left(i\right)y$ intercept is $-\frac{3}{2}$
$\left(ii\right)x$ intercept is $4$

Answer 1

$\left(i\right)$ Given, $m=\tan \theta =\frac{1}{2}$
$c=y$- intercept = $-\frac{3}{2}$
We know that equation of line is $y=mx+c$
$\Rightarrow y=\frac{1}{2}x+\left(\frac{-3}{2}\right)$
$\Rightarrow y=\frac{1}{2}x-\frac{3}{2}$
$\Rightarrow 2y=x-3$
$\Rightarrow 2y-x+3=0$
Hence, the required equation is $2y-x+3=0$

$\left(ii\right)$ Given, $m=\tan \theta =\frac{1}{2}$
$d=x-$ intercept $=4$
We know that equation of line is $y=m(x-d)$
$\Rightarrow y=\frac{1}{2}(x-4)$
$\Rightarrow 2y=x-4$
$\Rightarrow 2y-x+4=0$
Hence, the required equation is $2y-x+4=0$