No. It means that the object is going at a constant speed.
Straight line
A straight horizontal one does.
the slope would be speed.
a straight line with a positive slope
Yes. Speed is the rate at which distance changes over time. In calculus terms v = dx/dt, or the slope of the distance vs. time graph. If the slope of the distance vs. time graph is a straight line, the speed is constant.
If the line formed by the graph is straight, the speed is constant. A horizontal line would show the object as stationary.
the object is not moving
It is a measure of speed of the object, but only in the radial direction: that is, towards or away from the point from which distance is measured. The object could be going around that point in circular motion and the graph would show absolutely nothing.
In this case, you will have a straight line.
A straight line.
Straight line
no motion