From Hartley and Zisserman Multiple View Geomerty p. 69, regarding representations of a line in $\mathbb{P^3}$:
"Suppose $\mathbf{A}, \mathbf{B}$ are two (non-coincident) space points. Then the line jointing these points is represented by the span of the row space of the 2x4 matrix $W$ composed of $\mathbf{A^T}$ and $\mathbf{B^T}$ as rows:
$$ W^T = \begin{bmatrix} \mathbf{A^T}\\ \mathbf{B^T}\\ \end{bmatrix} $$
Then: The span of $W^T$ is the pencil of points $\lambda\mathbf{A} + \mu\mathbf{B}$ on the line.
Can someone help me understand why a line seems to be a two-dimensional space with two free parameters $\lambda$ and $\mu$? I assume it is related to the fact that each point is in its homogeneous representation.