6.6.a 6.6.b 6.6.c

Algebraic Relationships 6th Grade

Texas Essential Knowledge and Skills (TEKS): 6.6.a
identify independent and dependent quantities from tables and graphs;
Texas Essential Knowledge and Skills (TEKS): 6.6.b
write an equation that represents the relationship between independent and dependent quantities from a table; and
Texas Essential Knowledge and Skills (TEKS): 6.6.c
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.

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

\frac{1}{12}

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.

Algebraic Relationships

Texas Essential Knowledge and Skills (TEKS): 6.6.a

identify independent and dependent quantities from tables and graphs;

Texas Essential Knowledge and Skills (TEKS): 6.6.b

write an equation that represents the relationship between independent and dependent quantities from a table; and

Texas Essential Knowledge and Skills (TEKS): 6.6.c

represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.

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