Introduction

In this lesson, you will learn how to interpret coordinate-system graphs.

Once you understand how to read and plot points on a coordinate system, you have the tools to start interpreting data. Data is used in every industry when making decisions. It is very important to know how to understand data.

These videos illustrate the lesson material below. Watching the videos is optional.

• Interpreting Information on a Graph (03:32 mins) | Transcript
• Interpreting a Graph (Average Temperatures) (04:22 mins) | Transcript

Interpreting Information on a Graph

A graph is a visual way to display information. It allows you to effectively analyze data. For example, here’s a graph that shows a company’s profit over several years:

Figure 1

The x-axis represents the years that the company has been in business. The y-axis represents the profits, or the amount of money the company made through the end of each year. Notice that the values on the y-axis are in increments of 200.

This graph gives you a general idea of how the company has done each year. There are years where it earned more and years where it earned less. You won’t know the exact amount of profit the company had each year based on the graph, but you can estimate yearly profits. An estimate is a close guess based on the information provided. For 2005, the dot is somewhere between 700 and 800. A good estimate would be 750.

Figure 2

Now look at 2007. The dot is somewhere in between 1000 and 1200. You can estimate that the company made somewhere around 1130 or 1150.

Figure 3

This graph also tells you when the company made the most profit and when it made the least profit. The dot corresponding with the year 2008 has the highest y-axis value on the graph. It corresponds with the highest value in profit. Similarly, the dot corresponding with the year 2001 is the lowest on the graph. It corresponds with the lowest number on the y-axis and thereby the least amount of profit.

Figure 4

Graphs are also a great tool for showing trends. A trend is the general direction of something that is changing or developing.

Figure 5

Based on the information on this graph, it appears that this company is following a positive trend, meaning it is making more money as time goes on. Trends and profits are just two of the things that graphs can convey.

Example 1
The graphs below show the average temperatures in Verkhoyansk, Russia. This city has very extreme temperatures throughout the year. When is it coldest in Verkhoyansk?

To find the answer, consider the following information about the graphs:

• One portrays temperatures in Fahrenheit, and one graph portrays them in Celsius, but the information in both graphs is the same.
• The legend at the bottom of the graphs tells you that the highs are represented by orange dots, and the lows are represented by blue dots.
• 1 on the x-axis corresponds to January, 2 corresponds to February, and so forth. If you look at the Celsius graph, you see that the dot with the hottest temperature is near 23 degrees Celsius. That dot corresponds with month seven, which means July is the month with the hottest average temperatures. You see the same thing on the Fahrenheit graph; the hottest temperatures, about 73 degrees Fahrenheit, are in July.

Figure 6

When is it coldest in Verkhoyansk?

• On the Celsius graph, there’s a dot in January that is near -50 degrees Celsius.
• In Fahrenheit, it is near -55 degrees.

December gets close to that temperature as well, but based on these graphs, it looks like January is the colder month.

Example 2
You want to plan a trip to Verkhoyansk in April. What average temperatures could you expect? On either graph, you would go to month four (April) and look at the average temperatures.

• On the Celsius graph, the average high is around -3 degrees Celsius and the average low is around -21 degrees Celsius.
• On the Fahrenheit graph, the average high is about 24 degrees Fahrenheit, and the average low is around -5 degrees Fahrenheit.

Things to Remember

• Use the graph title and the legend to identify what information the graph is displaying.
• Identify the x-axis units and y-axis units from the information of the graph.
• An estimate is a close guess based on provided information.

Practice Problems

Use the following graph to answer questions 1 through 5.

1. Which of these spices comes in a container with the lowest number of ounces? (
   Solution

   x

   Solution: Thyme
   Details:
   You are comparing how many ounces are in each container, so you need to look at the corresponding measurements on the x-axis.
   
   
   You can approximate how many ounces by looking at the x-value for each spice. As you can see, the thyme has the lowest number of ounces.
   )
   
   1. Thyme
   2. Salt
   3. Sage
   4. Black Pepper
   5. Nutmeg
2. Which of the spices has the highest price per container? (
   Solution

   x

   Solution:
   Nutmeg
   )
   
   1. Thyme
   2. Salt
   3. Sage
   4. Black Pepper
   5. Nutmeg
3. Which spice is shown at the point (\(0.75, 5\))? (
   Solution

   x

   Solution:
   Oregano
   )
   
   1. Salt
   2. Oregano
   3. Black Pepper
   4. Cinnamon
4. What is the price of a container of garlic salt at this market (in dollars)? (
   Solution

   x

   Solution:
   About \($7.50\)
   Details:
   Since you are trying to find the cost of garlic salt, you need to find out the corresponding y-value. It helps to draw a horizontal line through the point representing garlic salt on the graph to estimate the cost per container.
   
   
   The dashed line crosses the y-axis at about \($7.50\), so you can estimate that this is the cost of the container of garlic salt.
   )
5. How many ounces are there in the container of cinnamon sold at this market? (
   Solution

   x

   Solution:
   About \(2.25\)
   )

Need More Help?

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