The equation of the line parallel to the line $ax+by+c=0$ and passing through origin is

Equation of the line parallel to $ax+by+c=0$ is

$ax+by+k=0$

But $(0,0)$ lies on $ax+by+k=0$

$a\left(0\right)+b\left(0\right)+k=0$

$k=0$

$\therefore$Equation of the line is $ax+by=0$