Dependent Variable
In short: Dependent variable is the result quantity in a two-quantity story, whose value gets settled once the other quantity has been picked.
6th GradeAlgebra6.EE.C.9
What is Dependent Variable?
The dependent variable is the answer that waits for the input. A phone battery drains as the minutes of video pass: the percentage left depends on the time, so the percentage is the dependent quantity.
Precisely, if a rule such as \(y = 6x + 2\) links two variables, the value of \(y\) is computed after \(x\) is chosen. The dependent variable is placed on the vertical axis of a graph and fills the second column of a table.
How to spot it
- A phrase says “depends on”, “is determined by” or “is a function of” another quantity.
- The quantity you calculate in a rule, such as total cost or distance traveled, is the target.
- A table has a second column that is filled by applying a rule to the first.
- A graph labels its vertical axis with an amount that grows or shrinks with time.
The method
- Ask which quantity responds when the other one changes.
- Give it a letter that suggests its meaning, like c for cost or d for distance, and state its unit.
- Put it alone on the left side of the rule, the way \(d = 12t\) is written.
- Place it on the vertical axis and compute its values from chosen inputs.
Dependent Variable: solved example
Problem
A tutoring center in Madison charges a $2 sign-up fee plus $6 per week. Write the rule for total cost c after w weeks, say which letter is the output, and find c when \(w = 9\).
Solution
The rule is \(c = 6w + 2\). The total depends on the number of weeks, so c is the dependent variable.
For \(w = 9\): \(c = 6 \cdot 9 + 2 = 56\). The cost is $56.
Try it
Question 1
A sprinkler uses 4.5 gallons per minute. In \(g = 4.5m\), which letter is the output?
Show the answer
g, the gallons, because it is computed from the minutes m.
Question 2
For the rule \(y = 3x – 1\), find y when \(x = 5\).
Show the answer
\(y = 3 \cdot 5 – 1 = 14\).
Dependent Variable vs. Independent Variable
Input versus output. The independent quantity is the one you pick or that runs by itself, drawn along the bottom edge of a graph. The dependent one is the result of that pick, drawn up the side.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · 6th Grade · Algebra