For a school project, I need to make a program that can plot $y = f(x,z)$ using a form of dimetric projection. I was given the projection formulae
$$\begin{align*} x' &= x + sz\cos(\theta)\\ y' &= y + sz\sin(\theta) \end{align*}$$
where $x'$ is the projected $x$-value, $x$ is the original $x$-value (in 3D space), $s$ is some constant (here it is $0.5$), $z$ is the depth in 3D space, and $\theta$ is an angle between $0^{\circ}$ and $90^{\circ}$ that represents the angle of 'pitch' from which the function is viewed, like
The program works fine, but now I have to write a document explaining why and how this form of projection works, and I'm completely stuck because nobody has bothered telling me why.
I get the general idea from my online wanderings, but I'm having issues understanding why it's OK to take a 3D shape and claim it can be projected using 3 axes on a flat plane at $120^{\circ}$ (or some similar value) and equate it to using 3 axes in 3D space like here:
and what the reasoning for the s value is.