Question

Find the equation of the line intersecting the y-axis at a distance of $3$ units above the origin and $\tan \theta =\frac{1}{2}$, where $\theta$ is the angle of inclination.

• A. $x-2y+6=0$
• B. $x+2y+6=0$
• C. $x-2y-6=0$
• D. None of these

Answer 1

The correct option is A $x-2y+6=0$

We have,

$\tan \theta =m=\frac{1}{2}$

Since, the line intersecting the $y-axis$ at a distance of $3$ units above the origin, it means $y=3$ and $x=0$.

So, the point $(0,3)$

We know that the equation of the line

$y-y_1=m(x-x_1)$

Therefore,

$y-3=\frac{1}{2}(x-0)$

$2(y-3)=x$

$2y-6=x$

$x-2y+6=0$

Hence, this is the answer.