Definition: The independent variable is the input that you choose or change, and the dependent variable is the output whose value depends on it.
What are the two variables?
In a relationship between two quantities, one changes by choice, and the other responds. The input is the independent variable. The output is the dependent variable.
How do you identify them?
Ask, which one depends on the other? Mathbot charges for time: a robot-wash costs 3 dollars per minute. The cost depends on the minutes, so minutes is independent (x) and cost is dependent (y). The equation is y = 3x.
How do you show them?
A table lists inputs and outputs. On a graph, the independent variable goes on the horizontal axis and the dependent variable goes on the vertical axis.
- x = 2 minutes gives y = 6 dollars
- x = 5 minutes gives y = 15 dollars
- x = 8 minutes gives y = 24 dollars
What can confuse you?
The roles can depend on the question. Asking how many minutes 36 dollars buys makes cost the input and time the output. Choose the variable you control or know first.
What is a common error?
Swapping axes, which flips the meaning of the graph.