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Because a slope of zero indicates that the y-value (speed) isn't changing.

Q: Why does a constant speed have a slope of 0 on a graph of speed v time?

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The graph is a straight line. Its slope is the speed.

It is 1 unit of distance per 1 unit of time.

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.

Slope at any point is speed. if slope is constant (staight line)then speed is constant; if curved up speed is accelerating. If curved down it is decelerating

The slope of the speed/time graph is the magnitude of acceleration. (It's very difficult to draw a graph of velocity, unless the direction is constant.)

Related questions

The graph is a straight line. Its slope is the speed.

The slope of the speed/time graph is the magnitude (size) of the object's acceleration.

At constant speed, the distance/time graph is a straight line, whose slope is equal to the speed.

It is 1 unit of distance per 1 unit of time.

The motion at constant speed.

constant

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.

Slope at any point is speed. if slope is constant (staight line)then speed is constant; if curved up speed is accelerating. If curved down it is decelerating

Motion at constant speed.

That would be true, in the case of a graph of speed vs time.

Constant

-- If the position/time graph is a straight line, then the speed is constant, and the slope of the line is the average speed, as well as the instantaneous speed at any moment. -- If the position/time graph is not a straight line, then the average speed between two moments in time is the slope of a straight line drawn between those two points on the graph.