back-projected ray in homogeneous coordinates

tdomhan

suppose I got a projective camera model. for this model I would like to back-project a ray through a point in the image plane. I know that the equation for this is the following:
$$
y(\lambda) = P^+_0 x_0 + \lambda c_0
$$
where [itex]P^+_0[/itex]denotes the pseudoinverse of the camera matrix.
[itex]x_0[/itex] the point on the image plane and $c_0$ the center of the camera. (This is taking from the book "Multiple View Geometry in Computer Vision" page 162)

Now I don't fully get this equation. I get that [itex]P^+_0 x_0[/itex] results in a point on the line we are looking for. Hence we have two points that we can use for constructing a line. However I don't get the parametrization using [itex]\lambda[/itex]. Why is the equation not in the form like:
$$y(\lambda) = (1-\lambda) a + \lambda b$$

Any help in understanding the original equation of the resulting ray would be appreciated! :D