What is a constant variation?

Constant variation, also known as direct variation or direct proportionality, is a relationship between two variables in which their ratio remains constant. In other words, as one variable increases, the other variable increases or decreases by a fixed factor.

Mathematically, if two variables x and y have a constant variation relationship, it can be represented by the equation y = kx, where k is the constant of variation. Here, k represents the constant ratio or proportionality between the variables.

Some key characteristics of constant variation are:

1. Graphical representation: When two variables have a constant variation relationship, their graph forms a straight line passing through the origin (0,0) on a Cartesian coordinate plane. This straight line is known as a direct variation or proportional line.

2. Proportional relationship: In constant variation, the variables are directly proportional to each other. This means that when one variable is multiplied or divided by a certain factor, the other variable undergoes a corresponding multiplication or division by the same factor.

3. Non-zero constant: The constant of variation (k) in a constant variation equation is always nonzero because division by zero is undefined. It represents the constant rate at which the variables change relative to each other.

4. Examples: Distance and time, mass and weight, and cost and quantity are some examples that can exhibit constant variation relationships. For instance, as time increases, the distance traveled in a constant speed situation increases at a constant rate.

Constant variation plays a significant role in various fields, such as physics, economics, and engineering, where many quantities are directly proportional to each other. It allows for easy comparison and prediction of how one variable changes as the other variable changes.