What is the price elasticity of demand equal to?

Elasticity of demand is defined as the ratio of percentage change in quantity demanded and percentage change in price.The mathematical expression for the elasticity of demand is given by (dQ/dP)* (P/Q). Along a linear demand curve, dQ/dP is constant but P/Q keeps on changing.

Now, consider a linear demand curve given by P = a - bQ------------(1)

Hence, the inverse demand is given by Q = a/b - P/b-----------(2)

Differentiating (2) with respect to Q, we get dQ/dP = -1/b---------(3)

Putting the value of (3) in (1), we get the elasticity equals to (-1/b)*(P/Q) which is not the same at all the points, i.e. it depends on the price quantity combination.