But what if the ONLY things you wanted to get across were:
PART I -- here is one kind of motion we care about.
1. When an object moves at a constant speed in a straight line, its position graph is a line.
2. In that case, the slope of that line stays constant. That slope is the speed.
3. Since the speed is not changing, the "velocity" graph is a horizontal line.
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The slope is the velocity not the speed. If the object were moving at a constant speed in the opposite direction the slope would be negative, the sign indicating the direction of the velocity vector in a 1D situation (which I'm assuming is what is happening here). Unless you only allow objects to move in the positive direction of how you oriented your coordinate axis.