If a relationship exists between two values, say x and y, such that one value, say y, is dependent on the other value, x, then x is referred to as the independent variable, and y is referred to as the dependent variable.
Consider a known relationship, such as the relationship between inches and feet.
There are 12 inches in 1 foot.
What if we want to know the number of inches in a given number of feet?
Then, the number of inches is dependent on the number of feet.
This relationship could be represented by the equation 12x = y, where x is the number of feet, and y is the number of inches.
In this situation, x is the independent variable and y is the dependent variable.
What if we want to know the number of feet in a given number of inches?
Then, the number of feet is dependent on the number of inches.
This relationship could be represented by the equation x = y, where x is the number of inches and y is the number of feet.
In this situation, x is the independent variable and y is the dependent variable.
Note that while you will often see the letters x and y used for the independent and dependent variables, respectively, it is the mathematical language and/or situation which dictates independent and dependent - not the letter used for the variable.
Mathematical relationships are often represented by equations, tables, and/or graphs.
The number of yards times 3 equals the number of feet.
So, an equation which could be used to find the number of feet based on the number of yards is 3y = f.
6th Grade Math - Algebraic Relationships Lesson