The independent variable is the input or quantity whose value is selected or varied, while the dependent variable is the output whose value changes in relation to it. In a context, table, graph, or linear equation, identify these roles from the relationship rather than assuming they are determined by labels; conventionally, the independent variable is on the horizontal axis and the dependent variable on the vertical axis, supporting later understanding of functions.
The independent variable is the input—the quantity you choose or change. The dependent variable is the output—the quantity that changes because of the input.
A taxi charges a fixed fee of $4 plus $2.50 for each mile traveled. The cost can be represented by
where is the number of miles and is the total cost.
Find the quantity being changed or chosen.
The number of miles, , can be different for each trip. It is the input.
Find the quantity that depends on it.
The total cost, , changes when the number of miles changes. It is the output.
Name the variables.
For example, if miles:
If the trip is miles:
The cost changes because the number of miles changes, so cost depends on miles.
On a graph, the independent variable is usually placed on the horizontal axis, and the dependent variable is placed on the vertical axis. Here, would be on the horizontal axis and would be on the vertical axis.
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