Slopes

The slope of a graph is equal to the change in the vertical between two points divided by the change in the horizontal; colloquially this is described as "rise over run".

In the graph on the right, the "rise" is the change in the $x$ value: $\mathrm{\Delta }x=-12\mathrm{m}$. The "run" is the change in the $t$ value: $\mathrm{\Delta }t=3\mathrm{s}$. Thus the slope of this line is $$\text{slope}=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=-4\frac{\mathrm{m}}{\mathrm{s}}$$

This quantity, displacement divided by a time interval, is the average velocity between the two points:

In this case, the slope is negative and so this object is moving to the left. Here is a more complicated position graph: