Question

Find the equations of the lines for which $\tan \theta =\frac{1}{\sqrt{2}},$ where $\theta$ is the angle of inclination of the line and $x-$intercept is $3$

Answer 1

$x-$intercept is $3$

Using slope intercept form, the equation of the line is $y=m(x-d)$

$y=\frac{1}{\sqrt{2}}(x-3)$

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

$\therefore$ equation of the line is $x-\sqrt{2}y-3=0$