I'm going to start with the basics here.  I know that you probably know this easy stuff...  But, I'm going to build up to something, so bear with me and follow along.

Let's look at the line passing through the points

( -2 , -1 )and( 4 , 3 )

 

Graph of a line that passes through the points ( -2 , -1 ) and ( 4 , 3 )  ...  rise from -2 to 4  ...  run from -1 to 3The simplest way to look
at the slope is

rise / run

(rise over run)

 

To get from the point
(-2 , -1) to the point (4 , 3), you rise up 4... 
and run over
6.

The slope is

rise / run = 4 / 6 = 2 / 3

Graph of a line that passes through the points ( -2 , -1 ) and ( 4 , 3 )  ...  up 4  ... over 6

 

Remember that, for rise / run...

You can "rise" up or down, but you ALWAYS "run" to the right!

rise (up and down) / run (over)