What are algebra variables? Why do they matter?

You're working on your algebra homework when you come across this word problem:

The relationship between screen time and sleep time is a linear equation where x is the screen time and y is the sleep time. Which is the independent variable and which is the dependent variable in the equation?

You may be familiar with the words "independent" and "dependent", but wonder how they could relate to algebra variables.

Let's take a closer look at some definitions and examples to help you answer this word problem.

Variable:

A variable is a symbol or a letter used to represent a value we don't know. Normally, "x" or "y" represents a variable, but other letters and symbols can represent an unknown.

Independent means:

• Not controlled by something else

• Its value "isn't changed by the other variables you're trying to measure"

Dependent means:

• Relying on other factors

• Its value depends on the value of other variables

Another way to define an independent variable is to say that "it does not rely (or depend) on another variable(s) to determine its value."

An example of an independent variable is the number of hours you study for a test, as it may affect your final grade. The hours are the independent variable because their value doesn't depend on another variable. Your final grade doesn't control how many hours you study.

If an independent variable doesn't rely on another variable, then a dependent variable relies on something else to determine its value.

Looking again at our example above of an independent variable, we can determine the dependent variable. The grade you receive may very well be directly affected by the number of hours you study. This means that the dependent variable is your final grade. The final grade depends on the number of hours you study.

So, why does it matter which variable is the dependent and which is the independent?

Knowing which one is which has to do with cause and effect. The independent variable is the cause, while the dependent variable is the effect. Knowing how to determine the cause and effect is "one of the most important parts of scientific research."

Example:

Your favorite candy bar costs $1.50 in the store. If you buy two, you pay $3.00 but if you buy four, you pay $6.00. Which are the independent and dependent variables?

The cost of the candy bar doesn't rely on anything else to determine its value — it will stay the same price: $1.50. However, the total cost of the candy bars will depend on the number of bars you buy.

The price of the candy bar is the independent variable and the total cost of candy bars is the dependent variable.

Another Example:

You're hooked on a TV show and can't wait to see the ending. Even though you need to wake up at 5:30 a.m., you stay up past midnight to finish the episode, only to find the episode ends on a cliffhanger, and you realize there’s more to watch the next night.

Determined, you stay up even later the next night, finally turning off the TV at 1:00 a.m. How did your screen time affect your sleep?

Let's first use our variables to represent the unknowns:

• Let "x" = the screen time you spent watching the show.

• Let "y" = your sleep time after watching the show.

If you spend two hours on screen time (past your bedtime), you get two hours less sleep. And if you spend three hours on screen time, you get three hours less sleep. The more screen time (x) you spend, the fewer hours of sleep (y) you get.

The screen time (x) doesn't rely on anything else to determine its value. However, sleep time (y) is controlled by the number of hours you spend watching TV. More screen time means less sleep but less screen time means more sleep!

To recap, our word problem stated:

The relationship between screen time and sleep time is a linear equation where x is the screen time and y is the sleep time. Which is the independent variable and which is the dependent variable in the equation?

Dependent variables have their value determined or controlled by something else. It's what you're changing — for example, the amount of sleep time after staying up late. Or, the amount of money you spend on buying candy bars.

Independent variables don't have their value determined or controlled by something else — For example, the number of hours you spend watching TV or the price of a candy bar.

The dependent variable is often represented by "x" while the independent variable is represented by "y".

If you'd like to learn more, discover other examples and definitions below!