The Scatchard equation is given by By plotting n/[L] versus n, the Scatchard plot shows that the slope equals to -1/Kd while the x-intercept equals the number of ligand binding sites n. When each receptor has a single ligand binding site, the system is described by with an on-rate (kon) and off-rate (koff) related to the dissociation constant through Kd=koff/kon.
When the system equilibrates, so that the average number of ligands bound to each receptor is given by which is the Scatchard equation for n=1.
Hence, by considering all n binding sites, there will ligands bound to each receptor on average, from which the Scatchard equation follows.
The Scatchard method is less used nowadays because of the availability of computer programs that directly fit parameters to binding data.
Mathematically, the Scatchard equation is related to Eadie-Hofstee method, which is used to infer kinetic properties from enzyme reaction data.