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# Line Graphs to Display Data Over Time

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

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Line Graphs to Display Data Over Time

Have you ever tried to show how something has changed using a graph? Remember Tania? Well, with all of the vegetables that she has been growing, Tania is trying to plan for next year. To do this, she takes a trip to the nearby organic farm to gather some data. When she meets with Mr. Jonas the farmer, he shows her a line graph that shows vegetable growth for the past four years. Tania is fascinated. Here is what she sees.

Mr. Jonas tells Tania that according to his calculations, the farm will produce twice as much in 2009 as it did in 2008. Tania leaves the farm with the data and a lot of excitement. She decides to redraw the line graph at home with the new calculations for 2009. The minute she gets home, she realizes that she is confused and can’t remember how to draw a line graph.

This is where you come in. There is a lot to learn in this Concept, pay attention so that you can help Alex draw his map and Tania draw her line graph at the end of the Concept.

### Guidance

Previously we worked on a few different ways to visually display data.

A line graph is a graph that helps us to show how data changes over time.

How can we make a line graph?

To make a line graph, we need to have a collection of data that has changed over time. Data that shows growth over years is a good example of appropriate data for a line graph.

When Jamal was born, his parents planted a tree in the back yard. Here is how tall the tree was in each of the next five years.

2003 2 ft.

2004 3 ft.

2005 5 ft.

2006 9 ft.

2007 14 ft.

Now let’s make a line graph.

The first thing that we need is two axes, one vertical and one horizontal.

The vertical one represents the range of tree growth. The tree grew from 2 feet to 14 feet. That is our scale. The horizontal axis represents the years when tree growth was calculated.

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 measures the same data as a line graph.

Solution: False. A line graph measures how data changes. A bar graph does not.

Now let's go back and help Tania with her garden plan. She wants to create a line graph to show the 2009 data with the other data she gathered from the farm.

The first thing that she needs to do is to draw in 2 axes.

The horizontal axis shows the years: 2005, 2006, 2007, 2008, 2009. The vertical axis shows the number of vegetables harvested. The highest number she has is in 2008 with 400 vegetables. However, the Mr. Jonas told her he expects to double this amount. This would give 2009 a total of 800 vegetables. Our range for the vertical axis is from 0 to 800 in increments of 100 units.

Here is Tania’s line graph.

### Vocabulary

Coordinate grid
a visual way of locating points or objects in space.
Coordinates
the x\begin{align*}x\end{align*} and y\begin{align*}y\end{align*} values that tell us where an object is located.
Origin
where the x\begin{align*}x\end{align*} and y\begin{align*}y\end{align*} axis meet, has a value of (0, 0)
x\begin{align*}x\end{align*} axis
the horizontal line of a coordinate grid
y\begin{align*}y\end{align*} axis
the vertical line of a coordinate grid
Ordered pair
(x,y)\begin{align*}(x, y)\end{align*} the values where a point is located on a grid
Line Graph
a visual way to show how data changes over time

### Guided Practice

Here is one for you to try on your own.

Look at the following line graph.

Which day of the week had the highest temperature? What was that temperature?

The day of the week with the highest temperature was February 3rd. The temperature on that day was about 33 degrees.

### Practice

Directions: Use the following line graph to answer each question.

1. What is being measured in this line graph?

2. What is on the horizontal axis?

3. What is on the vertical axis?

4. What was the highest temperature recorded?

5. What was the lowest temperature recorded?

6. What is the difference between the two temperatures?

7. On what day did the lowest temperature occur?

8. What was the average temperature for the week?

9. What was the median temperature for the week?

10. Did any two days have the same temperature?

11. What was that temperature?

12. On which two days did it occur?

13. Based on this trend, would the temperature on February 8th be less than 30 degrees or greater than?

14. True or false. There isn't a way to figure out the temperature on January 31st.

15. What was the temperature on February 5th?

### Vocabulary Language: English

$x-$axis

$x-$axis

The $x-$axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.
$y$ axis

$y$ axis

The $y$-axis is the vertical number line of the Cartesian plane.
Coordinate grid

Coordinate grid

The coordinate grid is formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate grid is also called a Cartesian Plane or coordinate plane.
Coordinates

Coordinates

The coordinates of a point represent the point's location on the Cartesian plane. Coordinates are written in ordered pairs: $(x, y)$.
Line Graph

Line Graph

A line graph is a visual way to show how data changes over time.
Ordered Pair

Ordered Pair

An ordered pair, $(x, y)$, describes the location of a point on a coordinate grid.
Origin

Origin

The origin is the point of intersection of the $x$ and $y$ axes on the Cartesian plane. The coordinates of the origin are (0, 0).