Let's use the examples in the last lesson...  We'll use the first one to find a formula.
 
the graph of a line passing through the points ( -2, -1 ) and ( 4, 3 ) We'll use the letter m
for slope.

m = rise / run  (rise over run)

 

Look at  rise/run  as  ( the change in the y's ) / ( the change in the x's ) = ( 3 - ( -1 ) ) / ( 4 - ( -2 ) ) = 4 / 6 = 2 / 3 the graph of a line passing through the points ( -2, -1 ) and ( 4, 3 ) ... We see that the change in the y's is the vertical change from one point to the other ... and the change in the x's is the horizontal change from one point to the other

Here's the official formula:

the graph of the line passing through the points ( x1, y1 ) and ( x2, y2 ) If you're given two points...  ( x1, y1 ) and ( x2, y2 ) ... m = ( y2 - y1 ) / ( x2 - x1 )