What is a proportional relationship?

A proportional relationship describes a relationship between two variables where their ratio is constant. This constant ratio is often called the constant of proportionality.

Key characteristics of proportional relationships:

• The relationship can be represented by the equation y = kx, where y and x are the variables, and k is the constant of proportionality.
• The graph of a proportional relationship is a straight line that passes through the origin (0,0).
• If one variable is multiplied by a factor, the other variable is multiplied by the same factor. This is the basis of direct variation.
• The ratio between corresponding values of the variables is always the same. This ratio is the constant of proportionality.

Examples of proportional relationships:

• The relationship between the number of hours worked and the amount earned, if the hourly wage is constant.
• The relationship between the distance traveled and the time taken, if the speed is constant.
• The relationship between the number of items purchased and the total cost, if each item has the same price.

Understanding proportional relationships is crucial in various fields, including mathematics, science, and economics, as they help us model and analyze situations where quantities change at a constant rate relative to each other.