Direct variation is a type of proportionality in which one quantity directly varies with respect to a change in another quantity, by the same factor. In other words, it is the relationship between two variables where one of the variables is a constant multiple of the other. Here are some key points to keep in mind:

• Direct variation exists between any two variables when one quantity is directly dependent on the other, meaning that if one quantity increases with respect to the other quantity, the other quantity will also increase, and vice versa.

• The direct variation equation is a linear equation in two variables and is given by y = kx, where k is the constant proportionality.

• The direct variation graph in a coordinate plane is a straight line passing through the origin.

• To solve questions on direct variation, the formula used is y = kx. If the constant of proportionality needs to be determined, then the given values of x and y can be used to calculate k.

• In direct variation, the variable that represents the cause of the relationship is called the independent variable, generally denoted by x. The other variable depends on the value of the independent variable and is called the dependent variable, generally denoted by y.

• The ratio between two quantities that are in direct proportion or direct variation always remains the same.

One example of direct variation is the relationship between the number of hours worked and the amount of money earned on an hourly pay basis. The more hours worked, the more money earned, and the ratio between the two remains constant.