Why and how do we use the graphs of linear equations?

Much as the road sign at the right can help you quickly understand a “falling rocks” hazard ahead, graphs are a useful way of conveying information visually. Graphs of linear equations are especially effective for representing relationships between things that change at a constant rate, and they often do a better job than words or mathematical equations alone.

Suppose your manager has asked you to create and present a financial report at the next company meeting. She wants to know how the amount of revenue your team brought to the company changed during the last year. Your job is to get the information and choose the best method for communicating it.

You start with a table showing the initial monthly revenue and the revenue earned in the odd numbered months:

The table is nicely organized, and its values are very precise, but it doesn’t readily show how the values change over time. So you study the numbers and try to describe this change in words:

Our team started the year with $1000 per month in revenue. For each additional month in the year 2015, our team produced an increase in $250 of revenue.

Next, you try expressing the information as a linear equation: [latex]y=250x+1000[/latex]

Again, both are very accurate, but neither reading two sentences out loud nor putting an equation on a poster board will go over very well with your manager or team members. You haven’t given them a way to picture the information. So, you try graphing the equation, which gives you the following:

Graph showing the linear relationship between time and the change in revenue.

All four—the table, the words, the equation, and the graph—are representations of the same thing. And, depending on your purpose, one representation may get your point across more clearly than another. As you can see, graphs are especially good at conveying information about the relationship between things (in this case, time and revenue) with very little explanation. Your graph shows that the revenue your team produced during the last year steadily increased—a very encouraging trend! You decide that the graph is definitely what you’ll present at the meeting.

In this module, you’ll learn how to create linear graphs in the Cartesian coordinate plane (like the one above) and why graphs are an especially useful means of conveying information.