The slope of a graph is given by [tex] \frac{\Delta y}{\Delta x} [/tex], or in English, the change in y divided by the change in x.
In the case of a distance-time graph, assuming distance is plotted on the y-axis and time on the x-axis, the slope would equal the change in distance divided by the change in time.
[tex] \frac{\text{distance}}{\text{time}} = \text{speed}[/tex]
So, speed is represented by the slope.
Another way of looking at this (and confirming it if you're ever unsure with a similar question) is by using dimensional analysis, which is a fancy way of saying 'look at the units'.
Distance is measured in metres (m), and time in seconds (s). The slope therefore would be equal to
[tex] \frac{m}{s} = ms^{-1} = \text{the unit of speed.}[/tex]
