# Linear & Nonlinear Relationships in Data Graphs

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• 0:02 What is a Science Experiment?
• 1:23 Linear and Nonlinear…
• 2:46 Lesson Summary

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain the difference between linear and nonlinear relationships when plotting graphs. A short quiz will follow.

## What Is a Science Experiment?

A science experiment is a way of figuring out the structure and behavior of the world using a systematic method. In a science experiment, there are always two variables we're investigating: we change one of them and then look at how it affects the other one. For example, we might look at how the amount of water affects how tall a plant grows. The amount of water is one variable, and the height of a plant is the other. Or we might look at how eating vegetables changes the feelings of well-being of a human as rated on a 1-10 scale. Here the mass of vegetables a person eats could be one variable, and the rating 1-10 could be the other. The key point is that there are two variables, and everything else should be kept the same. That way, you can really figure out if one things causes the other.

The scientific method is a way of conducting investigations to make accurate conclusions, using systematic observation, measurement, experimentation and modification of hypotheses. You conduct an experiment using a strict, reliable method, take measurements carefully and repeatedly in an experiment, analyze that data in a logical way and make conclusions from it. This is what science is all about. It's a process that we can use to figure out how the universe works. Once we have our data, it's time to analyze it. It's time to find the relationship between the two variables.

## Linear and Nonlinear Relationships

To find the relationship between two variables, we plot a graph. It's standard practice to put the variable you're actively changing on the x-axis (which is called the independent variable) and the result you're investigating on the y-axis (which is called the dependent variable).

Once you do that, you can plot your data and draw a line of best fit. Contrary to the way it sounds, a line of best fit can be a straight line, a curve or a mixture of both. The idea is that the line shows the clearest path through the data. Once you have a line of best fit, it's time to figure out the relationship between the two variables.

Using some mathematical (otherwise known as statistical) analysis, you can figure out what kind of graph your data creates. It might be a straight line graph (known by the function y = mx + b), or an x-squared curve, or an x-cubed curve, or a logarithmic relationship or something else.

But before you even run your analysis, plotting the graph will tell you a lot. Just looking at it, you can probably see if it's a straight line graph, like this one:

or a curve, like this one:

A straight line graph shows a linear relationship, where one variable changes by consistent amounts as you increase the other variable.

A curve graph shows a nonlinear relationship, where one variable changes by inconsistent amounts as you increase the other variable. You should be able to recognize whether a relationship is linear or nonlinear from a graph.

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