Question

Write equations of three lines, which pass through $(0,0)$.

Answer 1

Finding the equations of lines passing through $(0,0)$:

The equation of the line which passes through the origin is given in the form of $y=mx$.

where, $m$ is any constant.

substituting any value of $m$ we can get the required equations.

Let $m=2,3\&4$

So the three equations are:

$\left(i\right)$ $y=2x$

$\Rightarrow 2x-y=0$

$\left(ii\right)$ $y=3x$

$\Rightarrow 3x-y=0$

$\left(iii\right)$$y=4x$

$\Rightarrow 4x-y=0$

All these line passes through the origin because when we take $x=0$ we get $y=0$.

Hence, $2x-y=0$, $3x-y=0$ and $4x-y=0$ are the three solutions that passes through $(0,0)$.