Dependent and independent variables

Linear formulas and equations: Formulas

Dependent and independent variables

In the formula #\orange y=3 \cdot \blue x +4#, we call #\blue x# the #\blue{\text{independent variable}}#, because we can choose #\blue x# freely.‍

The variable #\orange y# is called the #\orange{\text{dependent variable}}#, because it is determined by the chosen value of #\blue x#.

Different letters

In formulas we usually use the letters #x# and #y#, but we can also use other letters.

In that case, the letter which is only on the left of the equals sign, without arithmetic operations, is the dependent variable. The letter which is to right of the equals sign, and which can be combined with all sorts of operations, is the independent variable.

Multiple independent variables

In a formula, multiple variables can appear on the right side of the equals sign. These are all called independent variables.

We can choose all of these variables freely. By choosing a value for all independent variables, we can calculate the dependent variable.

Examples

\[\begin{array}{rcl}\orange{y}=\blue{a}^2+3\blue{b}\\ \\ \orange{y}=\blue x \cdot \blue z +\blue z \end{array}\]

Look at the formula below
\[s=\left(u+2\right)\cdot \left(u+9\right)\]
Determine the independent variable and the dependent variable.

The independent variable is: #u#.
The dependent variable is: #s#.

After all, the independent variable is the variable that can be chosen freely, it is on the right of the equals sign and is in this case #u#.
The dependent variable is the variable determined by the chosen independent variable. It is always on its own and on the left side of the equals sign. In this case, that is #s#.

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