The relationship between two variables, say

*x* and

*y*, is

**proportional**if there exists a

constant, say k, such that

*y* equals k

*x*.

In a proportional relationship, the constant is

often referred to as the

**constant of proportionality**.

Consider the known relationship between inches and feet. There are 12 inches in 1 foot.

If we want to know the number of inches, *y*, in a given number of feet, *x*, we can use the equation *y* = 12x.

This equation represents a proportional relationship, and 12 is the constant of proportionality.

In some situations, this constant is referred to as the **unit rate**.

In this situation, the unit rate can be interpreted as 12 inches per foot.

Sometimes values are presented in a table.

How can we determine if a table represents a proportional relationship?

We have to determine if there exists a constant such that each output value is the product of the constant and the corresponding input value.

Recognize that each *y*-value is 10 times the corresponding *x*-value.

So, there is a constant, in this case 10, such that each *y*-value is the product of the constant and the corresponding *x*-value.

Therefore, the table represents a proportional relationship.