The equilibrium values themselves are not entirely arbitrary. The graph is drawn with the assumption that the following equations describe this market:

Demand P = 10 - 0.9Qd
Supply P = 0.5 + 0.5Qs

If we set Qd = Qs, and replace each of these variables with Q, then we have two equations (Demand and Supply) and two unknown variables (P and Q). In other words, we can "solve" for P* and Q*.

Setting the equations equal to one another, and solving for Q, we have:

10 - 0.9Q = 0.5 + 0.5Q
Q* = 9.5 units

Plugging Q* into either equation, we obtain the equilibrium price:

P* = 10 - 0.9(9.5) = $1.45