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no, a straight horizontal line doesn't indicates uniform motion
The answer depends on what you mean by "A".
It means that as time goes on, the distance increases quickly.
The straight horizontal line would indicate constant speed.(NOT constant velocity. The velocity could very well be changing, but the graphdoesn't tell you anything about the direction of the motion, only that the speedis constant.)
Yes. If it is not straight, then it is not a line.