The slope and elasticity of a linear demand curve are extremely closely linked, but where the slope itself is just a measure of how much demand changes given a change in price, elasticity is a description of what that slope means. Elasticity relates slope to the profitability of price changes.
A linear demand curve means that a change in price in any direction brings about a linearly proportional change in demand. If a 5 percent increase in price results in a 10 percent decrease in demand, a 10 percent increase in price results in a 20 percent decrease in demand. The slope of a linear demand curve is usually negative. The slope represents how quickly demand decreases with an increase in price.
A slope with a low magnitude represents an inelastic demand. This means that demand remains high despite an increase in price. Elastic demand, on the other hand, changes easily, and is represented by a steep linear demand curve. This means that an increase in price creates a relatively large decrease in demand. Elasticity is calculated by dividing a resulting percent change in demand by a given percent change in demand. A quotient over one is said to mean that the demand curve is elastic, while a quotient under one indicates inelasticity.