Question

The displacement-time graph can never be a straight line parallel to x axis. Why?

Answer 1

It can be parallel to x axis ( here it is time )
That means If it is parallel to the time axis, then the velocity of the particle is constant.
The slope at any point to the graph gives the velocity at that point or at the instant of time. ...Displacement parallel to the time axis implies the particle or object is not moving from its current position. Therefor its velocity is zero ( eg: A person walks for 2 minute and stays there and as time goes on his displacement doesn't changes)