No, in the Cartesian coordinate system it would show a vertical line whose intersection of the x-axis is 4.
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if the speed is zero then the distance versus time line will be horizontal
It would be a horizontal line, with a y-coordinate at the starting distance.
Distance and Time are variables and always moving. Therefore the answer is no. Let's suppose: If time is the vertical axis and distance (travelled) the horizontal axis. Standing still (not travelling) would show a vertical graph line. If distance is the vertical axis and time the horizontal axis. Then standing still would form a horizontal line based on time alone.
as a horizontal straight line
yes