Dependent Variable

Sommaire

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.

Each output c is found by applying the rule to its input w.

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.

Independent Variable

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Lessons

Independent and Dependent Variables

Worksheets and quizzes

Related words

Whole dictionary: A–Z · 6th Grade · Algebra

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