A graph requires two numerical variables before it can have a meaningful slope. A distance-graph has only one variable so it does ot have a slope in any meaningful way.
For eaxmple, you could have a graph showing the distances of varoius places from, say London.
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Slope of the graph will give you speed.
Because it does. :)
Examples of slope: http://www.answers.com/topic/slope http://en.wikipedia.org/wiki/Slope
If I walk 4 kilometers in an hour, my average speed during that hour was 4 km/hour. My instantaneous speed may well have been faster at times, and slower at other times, 4 km/hour is only the average.
if there is a slope, the velocity is either increasing or decreasing. This is acceleration.