Pre-Algebra
Expressions and equations
Dependent and independent variables
20 practice questions
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Theory + worked examples
Dependent and Independent Variables
Texas Pre-Algebra (TEKS) • Standard 6.6(A) • Expressions & Equations
Dependent and Independent Variables is a topic in Expressions & Equations in the Texas Essential Knowledge and Skills. It is aligned to Standard 6.6(A), which requires students to distinguish independent and dependent variables and relate them.
The independent variable is the input you choose; the dependent variable is the output that depends on it.
Theory
The independent variable is the input; the dependent variable is the output that depends on it.
\(y\) depends on \(x\): \(x\) goes on the horizontal axis, \(y\) on the vertical.
A table of related variables.
Telling them apart.
Relationship:
\[y=f(x):\ y \text{ depends on } x\]
Independent on the \(x\)-axis, dependent on the \(y\)-axis.
How to identify the variables
- Ask which quantity you control — that is independent.
- The one that responds is dependent.
- Independent goes on the \(x\)-axis.
- Write \(y\) in terms of \(x\).
Example 1 — Identify
Pay depends on hours worked. Which variable is dependent?
Solution
Pay responds to hours, so pay is dependent.
Example 2 — Independent
In Example 1, which is independent?
Solution
Hours worked — you choose it.
Example 3 — Equation
Write the equation if pay is \(\$12\) per hour.
Solution
Pay \(y\) depends on hours \(x\).
| \(y\) | \(=\) | \(12x\) |
Example 4 — Which axis
Which variable goes on the \(x\)-axis?
Solution
The independent variable.
Common pitfalls
The dependent variable responds; it does not drive.
Independent on the \(x\)-axis.
Cause is independent, effect is dependent.
Frequently asked questions
What is the independent variable?
The input you choose.
What is the dependent variable?
The output that depends on the input.
Which goes on the x-axis?
The independent variable.
In y = 12x, which depends?
\(y\).
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