It's called the origin; the center of a graph.
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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.
It is not possible to answer the questions since there is no such thing as a zero axis.
a horizontal line
As the slope get closer to zero, the graph becomes close to horizontal.
For motion at constant speed along a straight line, the acceleration is zero.