Proportional vs Nonproportional Relationships

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

A non-proportional relationship is a relationship between two quantities where the ratio is not constant.

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

If a graph does not pass through the origin, it indicates that the relationship is non-proportional.

In a proportional relationship, the slope of the line represents the constant ratio between the two quantities.

A table of values is proportional if the ratios of corresponding values are constant.

An example of a proportional relationship is the relationship between distance and time at a constant speed.

An example of a non-proportional relationship is the relationship between the number of items purchased and the total cost when there is a fixed fee.

A linear relationship is one that can be represented by a straight line on a graph.

The formula for a proportional relationship can be expressed as y = kx, where k is the constant of proportionality.