In the previous section, you investigated the differences between independent variables and dependent variables. The situations that you examined were presented in verbal form.

Did You Know?

Equations can be written in a form like this:

y = 2x – 10

or in function notation:

f(x) = 2x – 10

Function notation is read “f of x” and is shorthand for “function of x.” Function notation gives you a good clue about which variable may be the independent variable or the dependent variable.

Independent and dependent variables are also important with equations and functions that are presented in symbolic form with letters and numbers.

You will often see functional relationships written as formulas. Formulas are useful for expressing the relationship between variables used to make calculations.

For example, you may use formulas to calculate area, surface area, or volume.

You may also use formulas to calculate financial quantities, such as simple interest or compound interest. You may even use formulas to compute sales tax.

Interactive exercise. Assistance may be required. Match each dependency statement with the function it best describes. You may use some functions more than once or not at all.

How can you identify the independent variable in an equation or a formula?

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Look at the list of equations next to their descriptions in the completed interactive. What patterns do you see? Close Pop Up

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Check Your Answer

The independent variable is operated on with mathematical operations (multiplication, addition, exponents, etc.) in order to generate the value of the dependent variable. Close Pop Up

Can a formula have more than one independent variable? Why or why not?

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Look at the formulas in the list in the interactive. Do any of them have multiple variables on one side of the equal sign? Close Pop Up

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Check Your Answer

Yes. Some formulas take several independent variables, operate on them (multiply, add, etc.), and generate the value of the dependent variable. Close Pop Up

Practice

  1. The area of a square is represented by the formula A = s2. Which variable represents the independent quantity in this relationship?

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    Which variable represents the part of the square that you would measure, and which variable represents the quantity that you would calculate? Close Pop Up

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    Check Your Answer

    s, the side length of the square, is the independent quantity. Close Pop Up

  2. The distance that a car can travel on a certain number of gallons of gasoline can be found using the equation m = 24g, where m represents the number of miles and g represents the number of gallons. Which variable represents the dependent quantity in this relationship?

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    Which variable is controlled by the other variable? Close Pop Up

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    Check Your Answer

    The number of miles is dependent on the number of gallons of gas. Close Pop Up