Afraid I will need a bit more information before I can answer for sure, but the term k, in algebra, stands for constant of variation. In the equation y = kx, k is the constant of variation. So if you have an ordered pair (2,4) where x = 2, y = 4, then k = y/x or 4/2. So k = 2 in this case. Then the equation y = kx becomes y = 2x.
If you are referring to a Mobius strip (see your word entry at top: Moebius), then ignore my comment above and see the link below. Here is an excerpt from the Wikipedia article. k still refers to slope, but the explanation is a bit more complex.
If both ρ and α are nonzero, then the transformation is said to be loxodromic. These transformations tend to move all points in S-shaped paths from one fixed point to the other.
The word "loxodrome" is from the Greek: "λοξος (loxos), slanting+ δρόμος (dromos), course". When sailing on a constant bearing - if you maintain a heading of (say) north-east, you will eventually wind up sailing around the north pole in a logarithmic spiral. On the mercator projectionsuch a course is a straight line, as the north and south poles project to infinity. The angle that the loxodrome subtends relative to the lines of longitude (i.e. its slope, the "tightness" of the spiral) is the argument of k. Of course, Möbius transformations may have their two fixed points anywhere, not just at the north and south poles. But any loxodromic transformation will be conjugate to a transform that moves all points along such loxodromes.