A basic question about supply and demand graph
Yes, typically we would like estimate these curves’ functional forms. If we estimate a demand function $P=10-2Q$ we can rearrange it such that $Q=5-\frac{1}{2}P$. 

This, just changes the way we interpret the relationship. For a given quantity how does price change? Compared to, for a given price how does quantity change? This begs even further questions however because in the market we typically just observe equilibriums and “shocks” that determine prices typically also affect quantity. This makes estimating these functional forms difficult from an econometrics point of view.