How does a distance-time graph's slope show speed?

A distance-time graph records how far a traveler has gone as time passes. Here time is measured in seconds on the horizontal axis and cumulative distance in meters on the vertical axis. Cumulative distance adds the path traveled; it is not a signed location that can decrease when direction changes.

Slope compares a vertical change with its matching horizontal change. In the first segment, distance increases by four meters over two seconds. The speed is therefore two meters per second. A higher point alone does not mean a faster current speed; the amount added per second determines the slope.

The next segment is horizontal from two to three seconds. No distance is added during that second, so the modeled speed is zero. In the final second, distance rises from four to six meters, again giving two meters per second. The straight segments state constant speeds within their intervals.

The entire journey covers six meters in four seconds, giving average speed 1.5 meters per second. The pause contributes time even though it contributes no distance. Every optional journey keeps the same axis scales, so changes in the drawn slopes reflect the stated rates rather than a rescaled graph.