Key takeaway: The dependent variable is the output quantity whose value is determined by another quantity, called the input, and it is shown on the vertical axis of a graph.
Grade 66.EE.C.9Expressions and Equations
Definition of Dependent Variable
The dependent variable is the quantity that reacts. Its value is set by the other quantity in the relationship, so if you know the input, you can work out this output.
On a highway at a steady 62 miles per hour, the distance driven \(d\) depends on the hours \(h\) of driving. Distance is therefore the dependent variable, and time is the independent one. In an equation it usually appears alone on one side, as in \(d = 62h\). In a table it fills the output column, and on a graph its values are read up the vertical axis.
Formula and notation
A rule that gives the output from the input looks like
\[d = 62h\]
where \(h\) is the input and \(d\) is the output. Changing \(h\) forces \(d\) to change; the reverse is not how the rule is read.
Key facts
- The output column of a table lists its values.
- On a coordinate graph, it is measured on the vertical axis.
- One input gives exactly one output when the relationship is a function.
- Reading the sentence “y depends on x” names y as the dependent variable.
Dependent Variable example
On a highway trip at a steady 62 miles per hour, the distance is \(d = 62h\). Name the dependent variable and find its value after 2.5 hours and after 4 hours.
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The distance \(d\) is determined by the time \(h\), so \(d\) is the dependent variable.
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For \(h = 2.5\): \(d = 62 \times 2.5 = 155\).
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For \(h = 4\): \(d = 62 \times 4 = 248\).
The dependent variable is \(d\); the distances are 155 miles and 248 miles.
Common mistake
Watch out
Theo graphs distance on the horizontal axis and hours on the vertical axis.
Why it is wrong
The convention puts the input on the horizontal axis and the output on the vertical axis. Here the output is distance, which depends on hours, so hours go along the bottom and distance goes up the side.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Expressions and Equations