Price Elasticity of Demand for a Straight Line Demand Curve:

The price elasticity  of  demand is not the same along a downward sloping straight line demand curve.   For a linear demand curve sloping downward from left to right, the price elasticity of demand starts from infinity (∞) at the point where the demand curve cuts the price axis and falls as we move downward to the right along the curve to zero at the point where the demand curve cuts the quantity axis.

At the price intercept, demand is perfectly elastic.  At the mid-point of the demand curve, demand is unit elastic.  At the quantity intercept, demand is perfectly inelastic.  Between the price intercept and mid-point of the demand curve, demand is elastic while between the mid-point and the quantity intercept, demand is inelastic.