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 $P^+_0$ denotes the pseudoinverse of the camera matrix. $x_0$ the point on the image plane and $c_0$ the center of the camera.

Now I don't fully get this equation. I get that $P^+_0 x_0$ 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 $\lambda$. 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