Identify independent and dependent variables

Independent and dependent variables describe the roles of two quantities in a relationship: the independent variable is the input or quantity that is selected or changes, while the dependent variable is the output whose value changes in response. In tables, graphs, equations, and real-world situations involving linear relationships, identifying these roles helps determine which quantity belongs on each axis and supports interpreting rates of change and making predictions; “independent” does not mean unrelated or necessarily causal.

Detailed Explanation: Identify independent and dependent variables

When two quantities are related, ask:

What quantity is chosen or changes first? This is the independent variable.
What quantity changes in response? This is the dependent variable.

A helpful question is: “Does this quantity depend on the other one?”

Example

A movie ticket costs 5 $. Let$ x $be the number of tickets bought, and let$ y$ be the total cost.

Find the input.
The number of tickets can be chosen: you might buy $1$ , $2$ , or $3$ tickets.
Therefore, $x$ , the number of tickets, is the independent variable.
Find the output.
The total cost changes depending on how many tickets are bought.
Therefore, $y$ , the total cost, is the dependent variable.
Check the relationship.
The equation is

y=5x.

If $x=3$ tickets, then

y=5(3)=15,

so the total cost is 15$.

The number of tickets is the input, and the total cost is the output. In a graph, put the independent variable on the horizontal $x$ -axis and the dependent variable on the vertical $y$ -axis.

Learn by doing: Identify independent and dependent variables

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

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