Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, one variable is always a constant value times or divided by the other variable, and this constant value is called the constant of proportionality. If the ratio between two variables is always the same, the relationship is proportional. Conversely, if the ratio changes, the relationship is not proportional.

Proportional relationships are closely related to linearity). Two quantities vary directly with each other in a proportional relationship, and the ratio between them always stays the same. The graph of the proportional relationship equation is a straight line through the origin.

To determine if a relationship is proportional, one should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional.

Examples of proportional relationships include:

• The relationship between the number of eggs and cups of milk in a recipe
• The relationship between the side length and perimeter of a square
• The relationship between the distance traveled and the time taken to travel that distance at a constant speed)

Examples of non-proportional relationships include:

• The relationship between the number of eggs and cups of milk in a recipe where the ratio between the two variables changes
• The relationship between the number of people and the number of cars needed to transport them, as the ratio between the two variables changes depending on the number of people[[3]](https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-proportional-rel/v/introduction-to...