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 $y-$ intercept is $1$

Answer 1

Slope of the line is $m=\tan \theta =\frac{1}{\sqrt{2}}$

Using slope-intercept form, the equation is $y=mx+c$

$y=\frac{1}{\sqrt{2}}x+1$

$\Rightarrow \sqrt{2}y=x+\sqrt{2}$

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