Suppose a consumer has strictly convex preferences and her Engel curve for a good is a vertical line for some range of income.In that same income range, her demand curve for the good slopes down.

Engel Curve

A graphic representation showing how a consumer's demand for a good varies with income, keeping other factors constant.

Strictly Convex Preferences

Preferences where consumers always prefer mixtures of goods to extremes, demonstrating a consistent desire for variety.

Demand Curve

A graphical representation in economics that shows the relationship between the price of a good and the quantity of that good consumers are willing and able to purchase at varying price levels.