That article is quite confusing. I was taking it as meaning that P was supply and Q was demand and that their relationship is not always linear due to other factors. For example, the price of gas has gone up how much in the past four years in the US? How much has the demand varied? If the relationship is not linear, what other factors could be coming into play?
The two equations describe the two lines in the usual supply & demand X-shaped plot. In a two-dimensional model, you are just talking about prices as a function of quantities. Since the observables are the Q & P at the intersection of those lines, to estimate the $$a$$ and $$b$$ parameters you twiddle the X and Y variables, and collect data from how the system responds. I think. I'm not an economist.
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