ag.algebraic geometry – Sections of (affine) toric varieties by linear subspaces

I am looking for a reference that expands on the following statement:

“Sections of toric varieties by linear subspaces defined by coordinates or differences of coordinates are binomial schemes.” (page 2 in “Binomial Ideals” by Eisenbud, Sturmfels, 1994).

Is there a source that expands on this point?

Are there other sources working out the sections of toric varieties by linear subspaces? I am looking both for explicit work akin to (Eisenbud, Sturmfels) as well as sources using intersection theory.

My motivation is to understand the linear subspaces contained in toric varieties arising in toric dynamical systems (Craciun, Gheorghe, et al. “Toric dynamical systems.” Journal of Symbolic Computation 44.11 (2009): 1551-1565.) because they have biophysical significance.