Say, for example, you have the vector $\vec {PQ} = \langle8,4\rangle$. As we all learned in Algebra I, the "traditional" slope (y-units per x-unit) would be $\frac{4}{8}$, and the slope for x-units per y-unit would be $\frac{8}{4}$.
This begs the question: Since we can find the x and y slopes, would it be possible to have a third variable (let's call it "z") for the iterator?
What I am trying to get at is this:
$$ \begin{array}{c|lc} z & \text{x} & \text{y} \\ \hline 1 & 2 & 1 \\ 2 & 4 & 2 \\ 3 & 6 & 3 \\ 4 & 8 & 4 \end{array} $$
Since I am dealing with a vector, how would I find the end size of z? For example, how would I go about determining that the end size of z in my example vector is 4, if I didn't know it before hand?
It seems as though you're referring to the parametrization of a curve (a line, in your case, but a curve more generally). Here's how it works:
We have a line, and in this case, it can be described by $y=\frac{1}{2}x$ or, possibly a bit easier for this circumstance, $2y=x$. Now, we come up with two functions $x(t)$ and $y(t)$ which describe the values of $x$ and $y$ for any value of a third variable $t$. Because of the way you've set this up, I'm going to say $y(t)=t$. Now, we can find the second function by noting that $x(t)=2y(t)=2t$.
At this point, we have enough to say that the line $2y=x$ is parametrized by the functions $x(t)=2t$ and $y(t)=t$, which we refer to as parametric equations. If you put these two functions into a vector as $\langle x(t),y(t)\rangle=\langle 2t,t\rangle$, it describes all vectors of this form, not just those you've listed in the table. However, if you'd like to iterate the vectors you're describing as a sequence, you can do so with the set $\{\langle 2t,t\rangle|t\in\mathbb{N}\}$.
As for your question about how to find the value of the iterator based on the vector, this actually tells you quite nicely, because we've already said that $t=y$.
If you want a little more info about this sort of thing, I'd look up a bit more about parametrization, if you haven't already. I believe MathByFives on YouTube has a few videos about parametrization, if you'd like something informative, but also silly and whimsical.