# How to Interpret & Construct Broken-Line Graphs

Instructor: Elizabeth Popelka-Brown
In this lesson, students will learn how to construct and interpret a broken-line graph. Specific concepts include representing variables on the axes, scale, breaks, and identifying trends.

## Representing Information Visually

Mike is CONSTANTLY hustling between tutoring jobs and cannot figure out why he's making so little progress paying off his credit card debt and student loans! Perhaps, if he organizes his financial situation into a simple, easy to understand graph, he'll get some insights. Let's explore how he might do that!

## Line Graphs

A good way for him to identify a trend, or pattern, in his finances might be to display data in a line graph, like the one shown here for plant height vs time. The graph shows that each day the plant's height increases by a centimeter. The graph forms a perfectly straight line. It's linear because the plant grows by the same number of centimeters each day.

In real life, data points usually don't increase or decrease by the same constant rate to make a perfectly linear graph. They will more likely form a broken-line graph, which is seen here.

Understanding how to build a broken-line graph helps us interpret the information it can provide, so let's look at how Mike built his.

## The Basics

There are some essential components that every line graph needs. You can see them in Mike's graph. First, it needs a title to describe the information contained in the graph. It also needs an x-axis, the horizontal line, and a y-axis, the vertical line. Both of the axes need to be labeled to show what they represent. Some months, Mike brings in more and spends more money, so his dollars are dependent on the month. Therefore, his dollars are the dependent variable, the one that goes on the y axis. In order to see the relationship between his income and expenses, he will graph them both on the same set of axes, thus resulting in a double broken-line graph.

## Creating the Scale

The scale of the y axis, the numbers representing dollars, ranges from \$500 to \$1150. This scale makes room for his monthly income, which varies from \$525 to \$1120. It also makes room for his expenses, which range from \$600 to \$1050. The interval of this scale is 50, which you can see by noticing that the number going up the grid increases by 50 each mark. He began his scale at \$500 because it would be silly to begin at 0 and use a lot of space to make his way up to \$525. He's placed a break symbol on the y-axis, below the 500, to indicate that he's skipping from 0 up to 500.

Now that he has the structure of the graph, he can begin adding data points. In January, he had \$1035 in income and \$825 of expenses. As you can see here, he added a J to the x-axis to represent the month. The dotted black arrow shows that he followed the vertical line that runs through the J up and placed a red coordinate half-way between the lines that marked 800 and 850, to show the expenses of 825. He then continued up the line to place a green coordinate a bit more than halfway above the midway point between 1000 and 1050, to show his income of 1035.

In February, he made \$1100 and spent \$975. Here, he has added the F along the x-axis to represent the month, a red coordinate to represent the \$975, and a green coordinate to represent the \$1100.

## Interpreting the Graph

As you can see here, Mike has completed his double broken line graph, so that he can begin to interpret the information it provides. Hopefully, he'll determine why he can't get himself out of debt!

The most helpful aspect of the graph is that it clearly highlights his biggest potential issue. The first four months, January - April, his income was comfortably more than his expenses.

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