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# Line Graphs

## Display given data as linear change on coordinate graphs.

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Line Graphs

Have you ever thought about tree growth?

Kelsey works at an arboretum. She tracks tree growth over time. Some trees grow at a faster pace than other trees. Here is some data on one of the trees in the arboretum.

2003 = 2 feet

2004 = 2.5 feet

2005 = 3.5 feet

2006 = 8.5 feet

2007 = 14 feet

If you were going to create a line graph for this data, could you do it?

This Concept is all about using line graphs to show how data changes over time. Pay attention to this Concept and you will know how to create this line graph at the end of the Concept.

### Guidance

Another way to look at data is through a line graph.

A line graph is a series of connected points that displays data or information that changes over time.

The line graph below illustrates the change in temperature over the first seven days in February in Boston, Massachusetts. Looking at the changes of the line, you can see that the temperature rose the first three days, February , , and . On February , the temperature began to decline. The temperature was the same on February and . The temperature began to rise again on February .

Now that you can see how the information is shown in a line graph, the next step is to learn how to make one yourself.

The population for the city of Los Angeles has been recorded on the data table below. Create a line graph to depict the population change from the year 1950 to the year 2000.

Year: Approximate Population:
1950 2,000,000
1960 2,500,000
1970 2,800,000
1980 3,000,000
1990 3,500,000
2000 3,700,000

To create a line graph:

1. Draw the horizontal and vertical axis.
2. Give the graph the title “Population of Los Angeles 1950-2000.”
3. Label the horizontal axis “Year.”
4. Label the vertical axis “Population.”
5. Look at the range in data and decide how the units on the vertical axis should be labeled. In this case, label the vertical axis 0 – 4,000,000 by five hundred thousands.
6. Plot the population for each year on the horizontal axis. For example, put a point at 2,000,000 to show the population for the year 1950. Above the year 1960, put a point at 2,500,000 and so on. Connect the points as you go.

Now that you have created a line graph, you can analyze the data and draw conclusions based on the reported statistics.

Looking at the line graph, what can you infer about the change in population from 1950 to 2000?

It is evident that the population has risen since the year 1950. You can see that the greatest change in population occurred from the years 1950 to 1960 and again from 1980 to 1990. You can see that the smallest change in population occurred between the years of 1990 and 2000. From 1990 to 2000, the population only grew by 200,000 people. Judging by the trend of the graph, you could predict that the population of Los Angeles will continue to increase over time.

The Electronic Energies Alliance recorded the average cost of one gallon of gasoline in the United States for the years 2000-2007. Present the information on the data table on a line graph.

Year: Average Cost of One Gallon of Gasoline
2000 $1.57 2001$1.10
2002 $1.46 2003$1.59
2004 $2.03 2005$2.25
2006 $3.30 2007$3.00

To create a line graph:

1. Draw the horizontal and vertical axis.

2. Give the graph the title “Change in Cost of Gasoline 2000-2007.”

3. Label the horizontal axis “Year.”

4. Label the vertical axis “Cost of Gasoline.”

5. Look at the range in data and decide how the units on the vertical axis should be labeled. In this case, label the vertical axis 0 – 3.5 by 0.5.

6. Plot the price of gasoline for each year on the horizontal axis. For example, put a point slightly above 1.5 to show that the cost of one gallon of gas in the year 2000 was $1.59. Place a point slightly above 1 to show that they cost of one gallon of gas in the year 2001 was$1.10. Use a straight edge to connect the points as you go.

Looking at the line graph, what can you conclude about the cost of gasoline from the years 2000-2007?

The price of a gallon of gasoline has increased approximately \$1.50 over eight years. You notice that the price of a gallon of gasoline dropped in the years 2001 and 2007, but increased in all other years.

Now let's practice with a few questions about line graphs.

#### Example A

True or false. You need a vertical and horizontal axis for a line graph.

Solution: True.

#### Example B

True or false. A line graph and a frequency table measure the same thing.

Solution: False. A frequency table measures how often something occurs. A line graph measures how data changes over time.

#### Example C

True or false. A bar graph compares data while a line graph shows how data changes.

Solution: True

Here is the original problem once again.

Kelsey works at an arboretum. She tracks tree growth over time. Some trees grow at a faster pace than other trees. Here is some data on one of the trees in the arboretum.

2003 = 2 feet

2004 = 2.5 feet

2005 = 3.5 feet

2006 = 8.5 feet

2007 = 14 feet

If you were going to create a line graph for this data, could you do it?

Here is the line graph to show Kelsey's data. Notice that the measurement of the tree in feet is the vertical axis. The years the tree height was recorded creates the horizontal axis.

This is our answer.

### Vocabulary

Bar Graph
a graph designed to compare data and show the frequency of the data.
Line Graph
shows how data changes over time.

### Guided Practice

Here is one for you to try on your own.

Look at Kelsey's tree growth line graph once again. If the same rate of growth occurs from 2007 to 2008 as did from 2006 to 2007, what will the new growth of the tree be in 2008?

To figure this out, we have to find the difference between the tree growth in 2006 and the tree growth in 2007. We can subtract to find this value.

The tree grew 5.5 feet from 2006 to 2007.

Now we can add that to the growth in 2007 to get the growth for 2008.

If the tree grows at the same rate, then the height of the tree will be 19.5 feet in 2008.

### Practice

Directions: Use this line graph to answer the following questions.

The vertical axis shows the number of vegetables harvested each year. This is recorded as vegetable growth. The horizontal axis shows the years vegetable growth was recorded.

1. How many vegetables were harvested in 2005?

2. How many vegetables were harvested in 2006?

3. What is the difference in growth from 2005 to 2006?

4. How many vegetables were harvested in 2007?

5. What is the difference in vegetable growth from 2006 to 2007?

6. What is the vegetable growth in 2008?

7. What is the difference in vegetable growth from 2005 to 2008?

8. If the vegetable growth follows the same pattern from 2008 to 2011, what will the new total be?

9. If there is a loss of 50 vegetables from 2008 to 2009, what will the new total be?

10. If there is a gain of 100 vegetables from 2008 to 2009, what will the new total be?

11. If there is a loss of 50% from 2008 to 2009, what will the new total be?

12. True or false. A bar graph shows the same data as a line graph?

13. True or false. A line graph must show how data changes over time.

14. - 15. Use a newspaper to find two line graphs. The business section is a good place to start. Examine the data and explain what the line graph represents to a friend.

### Vocabulary Language: English

bar chart

bar chart

A bar chart is a graphic display of categorical variables that uses bars to represent the frequency of the count in each category.
broken line graph

broken line graph

A broken line graph is a graph that is used to show changes over time. A line is used to join the values but the line has no defined slope.
continuous variables

continuous variables

A continuous variable is a variable that takes on any value within the limits of the variable.
data set

data set

A collection of these observations of the variable is a data set.
dependent variable

dependent variable

The dependent variable is the output variable in an equation or function, commonly represented by $y$ or $f(x)$.
discrete random variables

discrete random variables

Discrete random variables represent the number of distinct values that can be counted of an event.
independent variable

independent variable

The independent variable is the input variable in an equation or function, commonly represented by $x$.
Line Graph

Line Graph

A line graph is a visual way to show how data changes over time.
qualitative variable

qualitative variable

A qualitative variable is one that cannot be measured numerically but can be placed in a category.
quantitative variable

quantitative variable

A quantitative variable is a variable that takes on numerical values that represent a measurable quantity. Examples of quantitative variables are the height of students or the population of a city.
variable

variable

In statistics, a variable is simply a characteristic that is being studied.