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Identify independent and dependent variables

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.

Detailed Explanation: Identify independent and dependent variables

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.

Example

A taxi charges a fixed fee of $4 plus $2.50 for each mile traveled. The cost can be represented by

C=2.50m+4,C=2.50m+4,

where mm is the number of miles and CC is the total cost.

  1. Find the quantity being changed or chosen.
    The number of miles, mm, can be different for each trip. It is the input.

  2. Find the quantity that depends on it.
    The total cost, CC, changes when the number of miles changes. It is the output.

  3. Name the variables.

    • Independent variable: mm, the number of miles
    • Dependent variable: CC, the total cost

For example, if m=3m=3 miles:

C=2.50(3)+4=11.50.C=2.50(3)+4=11.50.

If the trip is 55 miles:

C=2.50(5)+4=16.50.C=2.50(5)+4=16.50.

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, mm would be on the horizontal axis and CC would be on the vertical axis.

Learn by doing: Identify independent and dependent variables

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Graphing - Scatter Plot (Linear) - Trend to Axis Name (Independent/Dependent)


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