In a velocity-time graph it will be the time axis (where velocity = 0).
On a distance-time graph it will be a line parallel to the time axis: distance = some constant (which may be 0).
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As, in the velocity-time graph, curves passes through zero means 'when time is zero velocity is zero'. Velocity is time derivative of displacement. So displacement is maximum or minimum when time is zero in position-time graph.
a horizontal line
If time is the x-axis as expected then the x-intercept would be zero movement of the velocity.
It is not possible to answer the questions since there is no such thing as a zero axis.
Yes. Zero velocity is a velocity; if it is always zero then it is a constant velocity.