In algebra, independent and dependent variables are two fundamental concepts used to understand the relationship between different quantities in mathematical equations and functions.
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Independent Variable:
- The independent variable is the variable that you can manipulate or change. It is often considered the "input" of a function. In many contexts, it is usually represented on the x-axis of a graph.
- For example, in the equation \(y = 2x + 3\), \(x\) is the independent variable. You can choose different values for \(x\) to see how they affect the output.
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Dependent Variable:
- The dependent variable is the variable that depends on the independent variable. It is the "output" of a function and changes in response to the independent variable. This is often represented on the y-axis of a graph.
- In the same equation \(y = 2x + 3\), \(y\) is the dependent variable. Its value depends on the value of \(x\). When you change \(x\), it results in a corresponding change in \(y\).
In summary:
- The independent variable is what you change or control (input).
- The dependent variable is what you measure or observe (output), which is affected by changes in the independent variable.
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