If an x-t graph is a position-time graph, velocity is the slope of the line on the graph.
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A velocity time graph is still a velocity time graph - no matter the degree of detail that you look at it.
Simply put, a velocity time graph is velocity (m/s) in the Y coordinate and time (s) in the X and a position time graph is distance (m) in the Y coordinate and time (s) in the X if you where to find the slope of a tangent on a distance time graph, it would give you the velocity whereas the slope on a velocity time graph would give you the acceleration.
The graph of velocity-time is the acceleration.
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).
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.