Line Graphs

Graphs help us display information in a visual manner, allowing everyone to understand exactly what we're trying to communicate. A set of random numbers might make our heads spin, but things become much clearer when we take these numbers and plot them into a graph. Line graphs are especially popular, and you've probably seen these graphs before. But why are line graphs useful? How do they help us interpret data, and how can we build our own line graphs? Let's find out:

What exactly IS a line graph, anyway?

As the name suggests, a line graph uses a line to literally "connect the dots." Each dot represents a different data point, and the line shows us how this data changes when subjected to different variables. Most of the time, this variable is time.

When are line graphs useful?

Line graphs are particularly useful if we want to display data that changes. And since our world is constantly changing, line graphs can help us visualize all kinds of different things.

Usually, the changing variable is time. For example, you might start out with $5 in your bank account. If you deposit $5 in your bank account at the end of every year, a line graph would show us a steady incline as the years go by. This is why line graphs are so popular in the financial world.

Line graphs can also focus on time. For example, you might have a line graph showing you how many Americans rely on glasses based on their age. Younger generations would be less likely to wear glasses, while older generations would be more reliant on glasses. This would also give you a line graph showing a steady incline.

On the other hand, line graphs can also display data that doesn't involve time. For example, if you had one printer you could only print one piece of paper at one time. If you have two printers, you could print two pieces of paper, and you could print three documents with three printers. If we plotted this on a line graph, we would get a steady incline that showed us the relationship between these two factors.

Building our own line graph

Let's build our own line graph. Imagine we had a friend named Russell, and we dutifully measured his height every third year on his birthday.

Create a graph with height on the "y" axis (the vertical line) and age on the "x" axis (the horizontal line). Next, let's put each of our measurements on the graph in the form of a dot.

The final step (and this is the fun part) is to connect the dots in one continuous line.

If we did this, we'd get a line graph like this:

Right away, we can see how useful a line graph can be. Instead of just looking at a set of numbers, we really get a sense of how data evolves over a period of time.

Take a closer look at what happens to Russell at age 12. That's right! He goes through a sudden growth spurt -- which is exactly what we'd expect at that age. This growth spurt continues throughout his teen years before tapering off and slowing down when he reaches his 20s.

If we did the same thing with other kids, we'd learn that they tend to go through a very similar growth pattern.

The difference between line graphs and line plots

Line plots and line graphs might sound like interchangeable terms -- but they''re not. Line plots (also known as dot plots) only feature dots with no connecting lines. Unlike line graphs, they don't work as well for communicating data that changes over time. Instead, we tend to use these graphs for constant, unchanging data. This data might involve the unchanging rules of physics or anything else that has always existed throughout time.

Getting complicated with line graphs

If you want to get fancy with your line graphs, you can put multiple lines on a single graph. To help us differentiate between the different lines, it's best to give each line a different color. For example, what if we wanted to compare Russell to his two friends David and Tom?

As long as we have the same reliable data for these two other individuals, we can put the heights of all three of them on the same line graph. We might keep Russell's line red while giving David and Tom yellow and green lines, respectively.

This gives us even more valuable insights because we can compare three different individuals very easily. We might see that David went through his growth spurt much later than Tom or Russell -- perhaps shooting up like a beanstalk at age 15. We might also see that Tom''s growth spurt ended much earlier compared to his friends -- perhaps reaching his full height by age 17.

We can use this same technique to compare all kinds of different data. This is especially popular and useful in the financial world, as it allows us to compare two (or three or four or more!) different investments and figure out which one is most profitable.

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Graphing Linear Inequalities in Two Variables

Flashcards covering the Line Graphs

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Practice tests covering the Line Graphs

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College Algebra Diagnostic Tests

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