According to Education Portal, the demand curve slopes down because price and the quantity demanded have an inverse relationship. This relationship is proven by the law of demand.
The law of demand states that as price increases, quantity demanded will decrease and vice versa. Consumers enforce this law by the substitution effect. Education Portal notes that people substitute goods if one good becomes cheaper relative to another good.
According to About.com, Giffen goods are goods that defy the law of demand as their quantity demanded and price are directly related. Both the law and the effect are visually represented in a demand schedule that shows quantity demanded at different prices. In turn, the demand curve is a visual representation of the demand schedule. Additionally, the price elasticity of demand signifies the responsiveness of quantity demanded to a change in price. A low elasticity (<1) indicates that consumers are not very responsive to a change in price and a high elasticity (>1) shows that their responsiveness is greater. Unit elastic (=1) proves that they have a constant response. Economists differentiate between changes in quantity demand and demand. The demand curve shifts at all given prices due to factors like population or income but quantity demanded is only price sensitive. Both concepts follow the ceteribus paribus or "all things equal" rule.