Independent Variable
In short: Independent variable names the starting quantity in a two-quantity story, the one set by a person or by the clock, with a second quantity reacting to it.
6th GradeAlgebra6.EE.C.9
What is Independent Variable?
Think of an independent variable as the knob you turn. In the story of a candle burning, time passes whether you like it or not, and the height of the candle responds to that passing time.
Precisely, in a rule that links two quantities, the independent variable supplies the inputs and is usually named \(x\). It is placed on the horizontal axis of a graph and in the first column of a table, and the other quantity is computed from it.
How to spot it
- A sentence says “depends on”, and the thing it depends on is the one you are looking for.
- One quantity is set by a person, a clock or a menu, such as hours worked or tickets bought.
- A table has an input column listed in order, like 1, 2, 3, 4.
- A graph labels its horizontal axis with time, distance or number of items.
The method
- Ask: which quantity could I choose freely, or which one just keeps going on its own?
- Name that quantity with a letter, such as t for time or n for number of boxes.
- Write the other quantity as a rule built from it, such as \(d = 12t\).
- Place the first quantity on the horizontal axis and the second on the vertical axis.
Independent Variable: solved example
Problem
A kayak rental in Maine costs $14 per hour. The total cost is \(C = 14h\). Which letter is the input, and what does a 3.5-hour trip cost?
Solution
The renter picks how long to paddle, so the hours h is the independent variable; the cost C depends on it.
For \(h = 3.5\): \(C = 14 \cdot 3.5 = 49\). The cost is $49.
Try it
Question 1
A plant grows 2.4 cm per week. In the rule \(g = 2.4w\), which letter is independent?
Show the answer
w, the number of weeks, since time passes first and growth follows it.
Question 2
On a graph, which axis usually carries the input quantity?
Show the answer
The horizontal axis, also called the x-axis.
Independent Variable vs. Dependent Variable
Think input versus output. This one is set by you or moves on its own; its partner is the result that follows. In \(d = 12t\), you pick t first, and only then is d settled.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · 6th Grade · Algebra