Both the slope of the demand curve and the elasticity of demand are measures of how consumers alter their quantities demanded in response to changes in price. How are the two concepts different from each other? Given a negatively sloped straight-line demand curve, how will slope and elasticity differ? Given a vertical or horizontal demand curve, how will they differ?

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The Answer is The slope of the demand curve relates absolute changes in price and quantity demanded. Elasticity is a ratio of percentage changes. Whereas the slope of the demand curve will depend on the units in which price and quantity are measured, elasticity is a pure number and is independent of the units in which price and quantity are measured.
If the demand curve is a straight line, its slope is constant. However, the elasticity of demand along a negatively sloped straight-line demand curve changes at every point. It increases as we move up on the demand curve (higher prices and lower quantities), and decreases as we move down (lower prices and higher quantities).
Finally in measuring slope, the change in price is in the numerator and the change in quantity is in the denominator. In the case of elasticity, the percentage change in quantity is in the numerator and the percentage change in price is in the denominator. Hence, if the demand curve is vertical (slope equals infinity), the elasticity of demand is zero (perfectly inelastic). If the demand curve is horizontal (slope equals zero), the elasticity of demand is infinite (perfectly elastic).

Both the Slope of the Demand Curve and the Elasticity