it will never be a vertical line as the slope is velocity and that would be infinite speed
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It is false
line graph
A line graph, not surprisingly!
It means there is no movement towards or away from the point from which distances are measured - usually the origin. The object can be moving in a transverse direction at any speed and the graph would not show it.
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.