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

and

 

The simplest way to look at the slope is (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

 

Remember that, for

...

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