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Because a slope of zero indicates that the y-value (speed) isn't changing.
The steepness of the line on a distance-time graph represents the radial speed of the object. That is, the speed with which the object is moving towards or away from the origin. The steepness takes absolutely no account of the transverse speed, so you can be going around the origin in a circle at a great speed but, since your distance remains the same, the D-T graph will be flat: implying speed = 0.
It is the point of origin of the x and y axes of the graph
On a speed time graph, the distance can be calculated by working out the area underneath the line. To work out the distance travelled between t=0 and t=10 you would need to find these two values and then work out the area on the graph of the shape bound by the line of the particle, the x axis, t=0 and t=10. The average speed of the particle is the distance (calculated above) divided by 10.
It indicates that the obect is moving, in a radial direct (towards or away from the point of reference) at a constant speed. That speed can be 0.