The slope of a line has a formula:
slope = m = (`y_(2)` - `y_(1)` )/(`x_(2)` - `x_(1)` )
The 2 and 1 stand for which point the number comes from. For instance, we could have:
Point 1 = (5,1)
Point 2 = (-2,3)
They can be switched, it wouldn't make a difference.
Then, plugging in the numbers:
m = (3 - 1)/(-2 - 5) = 2/-7 = -2/7
(If we had the numbers switched, then we would have had (-2)/7, neagtive on top, which would still be the same as -2/7)
For the second pair of points, following the same procedure:
m = (4 - -1)/(-1 - -1) = 5/0 = undefined.
So, I have heard teachers use different terms for this slope, undefined or no slope mostly. But, this isn't zero slope.
Good luck, Eli. I hope this helps.