I have two vectors $v = (v\_1,\ v\_2)$ and $w = (w\_1,\ w\_2)$, with $w, v \ \in K^2$ and $v \neq w$. The task is to find the (unique, if I understand the task correctly) affine subspace that contains both vectors.

The definition of a affine subspace $T$ is:

$T = x + U = \big\{ x+u|u \in U \big\}$, where $U \subseteq K^2$ and $x \in K^2$.

The task tells us to find the affine subspace which is a proper subset of K^2 ($T \subsetneq K^2$). The parts I do not understand: unique and proper subset. What if the two vectors are linearly independent, then any subset $U$ that contains them both must be equal to K^2.
Should I in this case construct $T$ by setting $x$ equal to one of the vectors and construct $U$ as the subset containing the other? But in this case the choice wont be unique or will it?

Question: How does one construct a unique (if unique is possible) affine subspace from the two vectors described above.