Slope and elasticity of demand have an inverse relationship. When slope is high elasticity of demand is low and vice versa.
When the slope of a demand curve is infinity, elasticity is zero (perfectly inelastic demand); and when the slope of a demand curve is zero, elasticity is infinite (perfectly elastic demand). Unit elasticity means that a 1% change in price will result in an exact 1% change in quantity demanded. Thus elasticity will be equal to one. A unit elastic demand curve plots as a rectangular hyperbola. Note that a straight line demand curve cannot have unit elasticity as the value of elasticity changes along the straight line demand curve. Virtual University
Inelastic demand curve PictureElastic demand curve Picture