Let us consider two planes with equations:

$P_1 : x + 2y + 3z = 3$ and $P_2 : 2x-y = 5$

By substituting $x$ as $0$, can I say that the point $(0,-5,13/3)$ lies on the line of intersection of two planes?

And if I find that the direction vector of the line of intersection is $(3,5,-5)$, Can I say that the equation of the line of intersection of two planes is $(0,-5,13/3) + t(3,5,-5)$ ?