Independent and dependent variables

Independent and dependent variables are related to each other using functions.

independent variable


An independent variable is not influenced by another variable. Independent variables represent the “input” value of a function, and are commonly denoted as x. They are sometimes called the “argument” of the function.


dependent variable


A dependent variable is determined by another variable. They are dependent on the “input” value. Dependent variables represent the “output” value of a function, and are commonly denoted as y. They are sometimes called the “value” of the function.

On a graph, the dependent variable is typically plotted on the y-axis and the independent variable is plotted on the x-axis.

Example

y = 2x

In the function above, y is the dependent variable, and x is the independent variable. If the value of x is said to be 1 (input), then the value of y will be 2 (output).

Example

If Nathan’s grade on a test increases by 10 points for every hour he studies, then his grade is dependent on the number of hours he studies. In this situation, Nathan’s grade is the dependent variable.

No matter what grade Nathan gets on the test, the number of hours he studies will not change. The number of hours Nathan studies is the independent variable.

The number of hours Nathan studies may depend on some other factor (e.g. his motivation, time spent playing video games, etc.), but in this scenario we are only examining the relationship between his grade and study time.