Can time ever be on the y axis?

In principle, time can be placed on the y-axis. This is, however, not very common when making graphs and it is primarily only done in special relativity when making Minkowski diagrams or spacetime diagrams.

Is X always time on a graph?

The x-axis is also called the independent axis because its values do not depend on anything. For example, time is always placed on the x-axis since it continues to move forward regardless of anything else.

Why is the x-axis always time?

The x-axis (horizontal) always shows the independent variable, that is the variable over which you have no control. This is most obvious when graphing distance and time. Time will always go on the x-axis, since it is independent of anything else.