It would help if we had the exact statement of the question, as well as, the level of rigor expected.
That said, here is my take on an answer.
If (a,b) is a point on the line y=2x-1 then b=2a-1. That is a true statement.
If (a,b) is a point in and b=2a-1 then (a,b) is on the line y=2x-1.
That is also a true statement.
But note the additional conditions I have added. That is what I mean by the level of rigor.
Sorry to say but this may not help you at all.