Math definition for "positive or negative" If you define a direction on a plane as either positive or negative, what would you call its positive/negativeness?  Its orientation?  I feel like there is a better word out there for this. 
So like, if there is an arrow that starts at (0,0) and has a slope of 1, and there is another arrow that starts at (0,0) and has a slope of -1, would I say, the first arrow is the same as the second arrow but with opposite orientation?  
 A: The word is sign:

In mathematics, the word sign refers
  to the property of being positive or
  negative. Every nonzero real number is
  either positive or negative, and
  therefore has a sign. Zero itself is
  signless, although in some contexts it
  makes sense to consider a signed zero.
  In addition to its application to real
  numbers, the word sign is used
  throughout mathematics to indicate
  aspects of mathematical objects that
  resemble positivity and negativity,
  such as the sign of a permutation.

On your arrows, if the gradients were +2 and -2 then they have opposite signs; if they were +2 and -0.5 they would be orthogonal or perpendicular. 
A: I would say direction.  The second arrow has the same slope as the first, but the opposite direction.
A: What you are describing here I think should be called a vector (as opposed to an "arrow"), so let's look at that definition from NOAD:

vector |ˈvektər|
  noun
  1 Mathematics & Physics a quantity having direction as well as magnitude, esp. as determining the position of one point in space relative to another.

It seems pretty clear we're talking about direction here. But in your example your vectors are not congruent, so each has a different location. It wouldn't be enough to say they have different directions. 
It is probably more accurate to say these are line segments with the same length and slope but different locations, or different start and end points, etc.
A: If you're looking for something that specifies some direction along a single dimension (either positive or negative) then positivity might work.
A: Polarity?  That might work for some applications.
