In the book Multiple View Geometry in Computer Vision, it says "a line is defined by the join of two points" in section 3.2.2
Later on it goes to say there is a point $P^+x$ (the point that projects to x on the image plane) and $C$ (the camera centre). And that the lined formed is the join of these two points (equation 6.13 in the book, page 162):
$$X(\lambda) = P^+x + \lambda C$$
How does adding the two create a line?
If you have a two point in cartesian coordinates say $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $\begin{bmatrix} 3 \\ 3 \end{bmatrix}$, then $\mu \begin{bmatrix} 1 \\ 2 \end{bmatrix} + \lambda \begin{bmatrix} 3 \\ 3 \end{bmatrix}$ does not form a line between those two points.
The parameter $\lambda$ runs through the set of real numbers. Every value of $\lambda$ defines a point on the line.
Please note that the book you are quoting does not seem to use Cartesian coordinates but projective coordinates. A point in projective 3-space is represented by a column of four numbers, not all of them 0, and two such columns represent the same point if and only if the columns are multiples of each other.
In such a coordinate system, the line joining two points can indeed be expressed by linear combinations with two real parameters $\lambda$ and $\mu.$