You have a motion graph for an object that shows distance and time. how does the slope of the graph relate to the object's speed?

The slope of a graph is given by , 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.



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