As stated earlier, the demand curve
is drawn with price on the vertical axis and quantity demanded (either by an individual or by an entire market) on the horizontal axis. Mathematically, the slope of a curve is represented by rise over run, or the change in the variable on the vertical axis divided by the change in the variable on the horizontal axis. Therefore, the slope of the demand curve represents change in price divided by change in quantity, and it can be thought of as answering the question "by how much does an item's price need to change for customers to demand one more unit of it?"
Elasticity, on the other hand, aims to quantify the responsiveness of demand and supply to changes in price, income, or other determinants of demand. Therefore, price elasticity of demand answers the question "by how much does the quantity demanded of an item change in response to a change in price?" The calculation for this requires changes in quantity to be divided by changes in price rather than the other way around.