The relationship between two variables, say
x and
y, is
proportionalif 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.
8th Grade Math - Proportional vs. Not Proportional Lesson