Example of straight line and a point in $\Bbb R^3$ such that there are infinitely many planes passing through it

Question

Give an example of a straight line $l$ in $\mathbb R^3$, given by a system of two equations, and a point $(a,b,c)\in \mathbb R^3$ such that there are infinitely many planes in $\mathbb R^3$ passing through $l$ and $(a,b,c)$. Justify your answer.

Straight line defined by $x−y=1,y−z=2$ and point $(1,2,3)$ (from a previous question) rather than point $(1,2,3)$ can we just give any point on the line because as long as its on the straight line there will be infinitely many planes?

Is this correct logic? its a strange question, I have never attempted one like this before so sorry if the answer is trivial.

Answer 1

That point isn't on that line (just plug it in).

Other than that, yes, you could take any point on the line.

Answer 2

can we just give any point on the line because as long as its on the straight line there will be infinitely many planes?

I'm not sure if this is enough of a justification or rigorous enough. It merely states that "the solution is correct, because it fullfills all requirements of the task", but it doesn't show how that's the case.