Skill: Identify dependent and independent variables

To identify the variables:

• The independent variable is the input—the value that is chosen or changed.
• The dependent variable is the output—the value that depends on the input.

Example

The total cost of a taxi ride is represented by

$$c=3m+2$$

where $m$ is the number of miles traveled and $c$ is the total cost in dollars.

Step 1: Find the input.
The number of miles, $m$, can change depending on how far someone rides. So $m$ is the independent variable.

Step 2: Find the output.
The total cost, $c$, changes when the number of miles changes. So $c$ is the dependent variable.

Step 3: Check the relationship.
If the taxi travels $4$ miles, substitute $4$ for $m$:

$$c=3(4)+2=12+2=14$$

The cost is 14$. The cost depends on the number of miles.

Answer:

• Independent variable: $m$, the number of miles
• Dependent variable: $c$, the total cost

Remember: Do not choose based only on the variable’s letter. Ask, “Which quantity is the input, and which quantity depends on it?”