Direct inverse joint and combined

Direct, inverse, joint, and combined variation are mathematical concepts that describe how variables relate to each other.

• Direct variation

  When two variables increase or decrease together at a constant rate. For example, the amount of money earned increases as the number of hours worked increases. 

 

• Inverse variation

  When one variable increases as the other decreases, or vice versa. For example, the amount of time to complete a job decreases as the number of people working on it increases. 

 

• Joint variation

  When a variable varies directly with the product of two or more other variables. For example, the area of a triangle is jointly related to both its height and base. 

 

• Combined variation

  When a variable depends on two or more variables, either directly, inversely, or a combination of both. For example, the average number of phone calls between two cities is jointly proportional to the populations of the cities, and inversely proportional to the square of the distance between the cities