Slope?????

Slope is defined to be rise / run

or:  the change in y / change in x

or:  m  =  (y2 - y1) / (x2 - x1)

For two points like (3, 5) and (12, 8) the slope is:  m = (8 - 5) / (12 - 3)  =  3 / 9  =  1 / 3,

so, for every run of 3, there will be a rise of 1, for every change in x of 3, there is a change in y of 1.

Now, let's try two points that lie on a vertical line:  say,  (7, 2)  and  (7, 12)

     --->  m  =  (12 - 2) / (7 - 7)  =  10/0  <--- this is undefined because you can't divide by zero

     --->  every vertical line has "no slope" or an "undefined slope".

Let's compare this to a horizontal line:  say,  (4, 5)  and  (21, 5)

     --->   m  =  (5 - 5) /(21 - 4)  =  0/17  =  0      

     --->  although there was a run of 17 (from 4 to 21), there was no rise (it started at 5 and ended at 5, it is              perfectly flat)

     --->  since zero is a number, every horizontal line has a slope, and its value is 0.

In this case "zero" doesn't mean "none"  

--->  "zero" means a flat line, a horizontal line

--->  "none" (or "no slope") indicates a vertical line