What-is-an-independent-variable-in-math

What Is An Independent Variable In Math? | A Quick Guide For Students

What is an independent variable in math? And why do we need an independent variable in an experiment or other places? Or do I even need to understand an independent variable? These are some of the questions that might arise in the students’ minds. 

Therefore, to help those students, I am here with a comprehensive guide on what is an independent variable in math. If you are afraid of mathematical concepts. Then keep in touch with Statanalytica. I always help you to make the concepts easily and effectively understandable. 

Apart from this, in today’s blog, I will help you understand the concepts of the independent variable. Below, I have mentioned some interesting examples that encourage you to learn. And know the independent variable concepts with ease. So, let’s get started.

What is an independent variable in math with example?

As the name itself suggests: 

“independent” => that doesn’t seem dependent on anything. 

In most cases, it has been seen that the independent variable is called the manipulated variable. The independent variable’s changes are not affected by any other kinds of variables. That is why we can say that either the changes can occur in the experiment on its own or the scientist can change the independent variables.

Let’s take the most common example of an independent variable:

It is easy to understand that time and age are the best examples of the independent variable. You can do nothing with time and age; neither you decrease or increase the value of time and age.

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Key points: 
An independent variable is one of the variables that use to represent the quantity, which is manipulated within the experiment.
X is the most used variable that represents the equation’s independent variable.

Why do we need an independent variable in an experiment?

It is a noticeable thing that an independent variable is used for checking the value of the network model prediction. Normalization importance plays an essential role. It is calculated using the important value that is divided by the largest importance value. Moreover, it is expressed as a percentage (%).

In simple words, we can say that an independent variable is useful to define other dependent variables. These dependent values can change as per the situations, like temperature and other factors. 

Apart from this, the independent variable uses to define the combined value or impact of the various dependent variables.

Let’s understand it with an example:

Suppose you have to calculate the speed of a car. As you know, speed = (distance/time), here we can say that speed is the dependent variable and distance and time are the independent variable. 

Distance and time can be varied independently. Like if you want to cover the distance of 15 km, you can cover it as fast as possible (by increasing speed) and as slow as possible (by decreasing speed). 

That is why distance and time are independent of each other, but the speed depends on both distance and time.

How do you write the independent and dependent variables in an equation?

You all might know that linear regressions for the two random variables depend on the linear equation. And this linear equation must consist of a single independent variable.

We write linear equation as:

y = a+b*x, 

=> In this equation, a and b are two constant numbers. Moreover, y is the dependent variable, and x is the independent variable.

If you draw the linear equation y = a+b*x, it will be a straight line.

NOTE: Keep in mind that you can select a value for substituting the independent variable. After this, it becomes quite easy to solve the dependent variable value.

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How do you find the independent variable?

Once you know what is an independent variable in math. It becomes easy to find the independent variable of an equation. Remember that the dependent and independent variable always draws in the equivalent places in the same graph. 

With the help of a graph, it is quite easy to check and understand which variable is dependent and which is the independent variable. 

NOTE: An independent variable is plotted on the horizontal axis or x-axis. Whereas the dependent variable plots on the y-axis.

Let’s understand it with an example: (A score graph of Enna)

In the above graph, it is remarkable that the score gets improved with increasing the study hours. Moreover, it is clear that studying for 6 hours can help Enna to get a higher score in her exams. But, when she studied for more than 6 hours, her score dropped slightly.

But, here, our motive is to make you understand what is an independent variable in math rather than understanding the reasons for dropping Enna’s score. 

So, by looking at the graph, you can understand that time considers as the independent variable that has been changed. Therefore, it is written on the x-axis. On the other hand, the score considers the dependent variable. And this score is plotted on the y-axis. 

This dependent variable changes as the value of the independent variable changes. So, this is how you can easily find out the independent variable by looking at the linear or algebraic equation’s graphs.

A brain booster

How do I know what is an independent variable in math just by looking at an equation?

Well, it is easy!!

But you have to be careful while finding the independent variable of an equation. 

Let’s take a look at the below example:

Suppose you have an equation x = 4+y

=> Here, you can see that x depends on the value of y and the constant term 4.
=> It means, as the value of the variable y changes, the value of x will also change. It implies that y is an independent variable as its value changes on its own.

But wait!!! What if the above equation changes to x – 4= y or y = x – 4.

Now, the same equation changes in an opposite way.

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How?

=> You can see that in the changed equation, y is the dependent variable, whereas x is an independent variable.
=> Moreover, the value of y changes as the value of x gets changed.

By looking at the above example, we can say that the independent variable is an individual or singular variable. The independent variable can take either side of “=” or equal to and with or without the constant term. 

Therefore, always be careful while deciding which is the independent and dependent variable by looking at the equation. Also, try to simplify or solve the equations before deciding on independent variables.

Test your knowledge about the independent variable!!!

Suppose you are assign to find out the best brand with the most kernel popcorn pops. You tested various popcorn brands’ bags to know the most kernel popcorn pops. 

So, what is the independent variable and dependent variable in this experiment?

Solution: 

Independent variable: Popcorn bag’s brands because you need to decide the particular brands of popcorn bags.
Dependent variable: The kernel pops are the things that you need to rank for each brand.

Conclusion

What is an independent variable in math is one of the searched questions. From this blog, it is quite clear that an independent variable is independent of changes. Moreover, it plays an important role in various experiments as it defines the combined impact of dependent variables.

Hope, I have answered your searched questions effectively. If you still have any  issue; please let me know through your comments. I will definitely provide you a quick guide related to your query in the best possible way. If you are not sure a about independent variable in math then take our math assignment help online. It will help you to clear all your doubts with the help of our maths solution online.

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Frequently Asked Questions

Which is the independent variable?

The independent variable is the variable that scientists can manipulate or change as per the situation. The variable also affects the dependent variable directly. Moreover, the dependent variables depend on the independent variable(s) in an experiment.

Is time a dependent variable?

No, time is an independent variable, and it does not affect by dependent variables such as environmental inputs and others. But the time is treated to be a controlled constant variable against which the system’s changes can be measured.

What is the independent variable between temperature and time?

It is clear that the temperature depends over time. Therefore, the temperature is taken as a dependent, whereas the time is taken as an independent variable.