The constant of proportionality is a number that describes the relationship between two variables that are directly proportional to each other. It is typically denoted by the letter k and is the ratio of the two variables. The constant of proportionality can be found using the equation k = y/x, where y and x are two quantities that are directly proportional to each other.

The constant of proportionality is also known as the coefficient of proportionality, the constant of variation, or the unit rate. It is used to determine the nature of proportionality, whether it is direct or inverse, and helps in solving equations involving ratios and proportions.

Examples of direct proportionality include the relationship between distance and time when an object travels at a constant speed, or the relationship between the circumference and diameter of a circle, where the constant of proportionality is equal to pi). Inverse proportionality occurs when the product of two variables is constant, such as the relationship between the speed of a moving vehicle and the time taken to cover a certain distance.

The constant of proportionality can be found from a graph by identifying any point on the line and calculating the ratio of the corresponding y and x values. It can also be found from a table by dividing any y value by its corresponding x value. Once the constant of proportionality is known, an equation representing the directly proportional relationship between the two variables can be written as y = kx.