Their Relationships

After reviewing this unit, you will be able to:

- Define the terms constant and variable.
- Identify whether an item is a constant or a variable.
- Identify whether an item is a dependent or independent variable.

In many introductory courses you will come across characteristics
or elements such as rates, outputs, income, etc., measured by
numerical values. Some of these will always remain the same, and
some will change. The characteristic or
element that remains the same is called a **constant**.
For example, the number of donuts in a dozen is always 12. That
means the number of donuts in a dozen is a constant.

While some of these characteristics or elements remain the
same, some of these values can vary (e.g., the price of a dozen
donuts can change from $2.50 to $3.00), we call these characteristics
or elements *variables*. **Variable** is the generic term for any characteristic or
element that changes. You should be able to determine which
characteristics or elements are constants and which are variables.

Which of the following are variables and which are constants?

- The temperature outside your house.
This is a variable. The temperature outside your home will change depending on the weather.

- The number of square feet in a room that is 12 ft by 12 ft.<
This is a constant. The square feet in a room 12 ft by 12 ft is always 144 square feet. It does not change.

- The noise level at a concert.
This is a variable. The noise level changes depending on the number of people talking and yelling at any given time.

(Click on the Practice button below.)

[practice]

We express a relationship between two variables, which we will
refer to as ** x** and

is an example of a relationship between *x* and *y*
variables. The equation also has an "a" and "b"
in it. These are constants that help define the relationship between
the two variables.

- In this equation the
variable is dependent on the values of*y*, a, and b. The*x*is the*y***dependent variable**. - The value of
, on the other hand, is independent of the values*x*, a, and b. The*y*is the*x***independent variable.**

The following is an example to illustrate how these equations are constructed.

Throughout this tutorial we will use an example
of a pizza shop that charges 7 dollars for a plain pizza with
no toppings and 75 cents for each additional topping added. The
total price of a pizza (** y**)
depends upon the number of toppings (

If we know that ** x**
(the number of toppings) and

We can set up an equation to show how the total price of pizza relates to the number of toppings ordered.

If we create a table of this particular relationship between
*x* and *y*, we'll see all the combinations of ** x** and

given:

yFinal Price |
a Plain |
b Price of Each Topping |
xNumber of Toppings |
---|---|---|---|

$ 7.00 | $ 7.00 | $.75 | 0 |

7.75 | 7.00 | .75 | 1 |

8.50 | 7.00 | .75 | 2 |

9.25 | 7.00 | .75 | 3 |

10.00 | 7.00 | .75 | 4 |

In the units that follow, we will review how this information can be displayed in the form of a graph. Before moving on, take a few moments to try the practice problem.

[practice] | [table of contents] | [next unit] |