I want to know about the galaxy is in linear motion
No, the galaxy does not move in a straight line.
https://en.wikipedia.org/wiki/Great_Attractor
The question is not clearly written, so I am unsure how to answer. The galaxy rotates around the core and moves through the local group. “Linear” is relative in many ways as it depends on your point of reference.
ditto. Linear motion in reference to what?