Algebra
Relations and functions
Independent and dependent variables
20 practice questions
2 video lessons
Theory + worked examples
Theory
In a relationship between two quantities:
- The independent variable is the input — you choose it (the \(x\)-axis).
- The dependent variable is the output — it depends on the input (the \(y\)-axis).
Ask “what depends on what?” The result is the dependent variable.
Input \(x\) determines output \(y\).
Identifying each variable.
The relationship:
\[y=f(x):\ x\ \text{independent},\ y\ \text{dependent}\]
The dependent variable is what you solve for.
How to identify the variables
- Find the two quantities.
- Ask which one depends on the other.
- The cause/input is independent (\(x\)).
- The result/output is dependent (\(y\)).
Example 1 — Distance and time
A car's distance depends on time. Name the variables.
Solution
Distance depends on time.
| \(\text{independent}\) | \(=\) | \(\text{time}\) |
| \(\text{dependent}\) | \(=\) | \(\text{distance}\) |
Example 2 — From an equation
In \(y=2x+1\), which variable is dependent?
Solution
\(y\) is found from \(x\).
| \(y\) | \(\text{depends on}\) | \(x\) |
Example 3 — Cost and hours
Pay depends on hours worked. Which axis is hours?
Solution
Hours is the input (independent), so the \(x\)-axis.
| \(\text{hours}\) | \(\to\) | \(x\text{-axis}\) |
Example 4 — Identify the dependent
Temperature rises with altitude changes. Which is dependent?
Solution
Temperature depends on altitude, so temperature is dependent.
Common pitfalls
The dependent variable is the output, the one you compute.
Independent goes on the \(x\)-axis, dependent on the \(y\).
“Depends on” points to the dependent variable.
Frequently asked questions
What is the independent variable?
The input you choose, on the \(x\)-axis.
What is the dependent variable?
The output that depends on the input, on the \(y\)-axis.
In \(y=3x\), which is dependent?
\(y\), since it is found from \(x\).
Which axis is the independent variable?
The \(x\)-axis.
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