Lesson Explainer: Line Graphs | Nagwa Lesson Explainer: Line Graphs | Nagwa

# Lesson Explainer: Line Graphs Mathematics

In this explainer, we will learn how to use line graphs to analyze data, communicate information, and get insights from data.

A line graph is a graph that uses points connected by lines to show how something changes, often, over time. Let us see how this works by drawing a line graph using data from a store selling ice cream in a seaside town. The table below shows the number of ice creams sold on four days in a particular week in June.

To draw a line graph, the first thing we need to do is to draw and label our axes. In this case, we have data on the number of ice creams sold (which will be on our vertical axis) and the day of the week on which those ice creams were sold (which we put on our horizontal axis).

Once we have our axes in place, from our data we can mark the number of ice creams sold each day on our chart. Here, we have done this with a cross. You can see, for example, that above “Thursday” there is a cross in line with where the number 12 would be on the vertical axis (since 12 ice creams were sold on Thursday).

We then join the dots in our plot with straight lines to give us the completed line graph.

Notice that in this graph each of the lines joining two crosses goes up, from left to right. This means that the ice cream sales increased each day. Suppose we now add the fact that 10 ice creams were sold on the following Monday to our data.

Adding this extra information to our line graph we see that the line between the sales figures for Sunday and Mondays goes down from left to right. This means that sales decreased from Sunday to Monday.

Let us now look at some examples of how we can use line graphs to analyze and gain information from data.

### Example 1: Reading Savings from a Line Graph

The line graph shows how much a person saved in each of the first four months of a year. In which month was the smallest amount of money saved?

To find out in which month the least money was saved, we can look on our line graph for the month that has the lowest point above it. In this case, you can see that the month of April has the lowest point above it. So, the smallest amount was saved in April.

### Note

By drawing a line directly across from the dot above April to the vertical axis, we can find out how much was saved in April. The line goes across to the number 10 on the vertical axis, so £10 was saved in April.

We can do the same for each of the months on the line graph

Now let us look at another example of reading and analyzing data from a line graph.

### Example 2: Reading Data from Line Graphs

The graph shows how much Farida had in savings at the end of each month, over a 5-month period. Find the difference in amount between when her savings were highest and when they were lowest.

The first thing we must do is to find out what Farida’s highest and lowest savings were. We can do this by looking for the highest data point on the line graph and the lowest data point on the line graph. The highest point is circled in blue and the lowest in pink, on the graph below.

The highest data point is above April and the lowest is above May. To find out what Farida’s savings were at the end of April and the end of May, we draw a line across to the vertical axis for each of these two months. We can then read off her savings for the end of April and the end of May.

The blue dashed line from the dot above April goes across to midway between 20 and 24 on the vertical axis. So, Farida had £22 in savings at the end of April. The pink dashed line from the point above May goes across to midway between 4 and 8 on the vertical axis, so Farida had (only!) £6 savings at the end of May. If we subtract Farida’s savings at the end of May from those at the end of April, we find that the difference between them is . Farida’s savings have therefore decreased by £16. This means that Farida must have spent £16 of her savings in May.

### Example 3: Interpreting Line Graphs

The graph shows Sarah’s total savings over seven weeks. Did she save more money from week 5 to week 6 than any other week?

We can work out whether or not Sarah saved more money from week 5 to week 6 than any other week in two different ways using the line graph.

Method 1

The first method is to work out how much Sarah had in savings each week across the whole seven-week period. We can then work out the weekly differences in savings amounts and decide which was the largest difference.

To read off the amount of savings Sarah had each week using the line graph, find the point above each week on the graph and draw a line across to the vertical axis. You can see in the graph below that, for example, Sarah had 150 dollars in savings in week 1. And in week 2, she had 140 dollars in savings.

Continuing in this way, we can work out how much Sarah had in savings in each of the seven weeks.

Now, to work out the weekly differences, we subtract the next week’s savings from the current week’s savings. For example, the difference in savings between weeks 1 and 2 was

This means that Sarah’s savings decreased by 10 dollars from week 1 to week 2. If we do this across all the weeks, we find all the weekly differences in savings.

We can see that the difference in savings between weeks 5 and 6 was 10 dollars, but the difference in savings between weeks 4 and 5 was 30 dollars. So, in fact, Sarah did not save the most between weeks 5 and 6. She saved the most between weeks 4 and 5.

Method 2

The second method we can use for this example is to look directly at the line graph to see if we can find which weeks had the largest increase in savings. So we are looking for the line with the steepest upward slope between two weeks.

There are three instances where the direction of the graph goes up from left to right, indicating an increase in savings. These occur between weeks 3 and 4, weeks 4 and 5, and weeks 5 and 6. We can see from the graph that the changes were as follows:

The largest increase was therefore between weeks 4 and 5, not weeks 5 and 6.

Let us look at another example of analyzing data using line graphs.

### Example 4: Analyzing Data from Line Graphs

The graph shows how much money a student had in their savings over 5 months.

1. How much did the student put into their savings in total over the 5-month period?
2. How much did the student take out of their savings in total over the 5-month period?

In order to solve this problem, first we need to know the amount of savings the student had each month. We can then work out the differences between consecutive months to find how much the student either put in or took out each month. A positive difference means the student saved that month and a negative difference indicates that the student took out money that month.

From the line graph, we can find the amount of savings the student had each month by mapping across, from each of the dots above the months, to the vertical axis. So, for example, mapping across from the dot above January, we can see that the student had £18 in savings in January.

Part 1

To work out the total amount the student saved over the 5 months, we need first to find out in which months the savings increased and by how much. We then add these increases together to give the total saved over 5 months.

We can tell if savings increased in a particular month because for an increase the line graph will slope up from left to right. There are two instances of this which are marked with pink arrows on the graph below.

We can see that savings increased between January and February and also between March and April.

We know that the student had £22 in February and £18 in January and the difference between these two is .

So, the student saved £4 between January and February. If we follow the same process for March and April, we find that the student saved between March and April. And adding these, we get the total amount the student saved, which is .

Part 2

To work out the total amount the student took out of their savings over the 5-month period, we need to work out in which months the savings decreased and by how much. Summing the decreases then gives us the total amount taken out over the 5 months.

A decrease is indicated on the line graph by a downward sloping line between two dots. There are two instances of this indicated on our graph below, between February and March and between April and May.

Between February and March, the student took out £12 and between April and May the student took out £10 from their savings. Adding these, the total amount the student took out over the five months was .

Let us look at one final example of how to gain information from line graphs.

### Example 5: Gaining Information from Line Graphs

The line graph below shows the number of cars parked outside a school on a Friday afternoon.

Use the line graph to answer the following questions.

1. How many cars were parked outside the school at 4 pm?
2. At what time were there 25 cars parked outside the school?
3. At what time was the least number of cars parked?
4. At which different times were the same number of cars parked?

Part 1

To find the number of cars parked outside the school at 4 pm, we map across from the point on the graph above 4 pm, to the vertical axis for the number of cars.

The number of cars in line with the point above 4 pm is 20. So, there were 20 cars parked at 4 pm.

Part 2

To find at what time there were 25 cars parked outside the school, we map across from 25 cars on the vertical axis and read down to the time from where we hit the line graph.

We hit the line graph at the point above 3 pm, so there were 25 cars outside the school at 3 pm.

Part 3

To find at what time the least number of cars was parked, we search the line graph for the lowest point.

The lowest point on the graph occurs above 6 pm. So the least number of cars was parked outside the school at 6 pm. Note that, reading across to the side axis, there were 3 cars parked at 6 pm.

Part 4

To find at which different times the same number of cars was parked, we need to see if there are any horizontal lines we can map across from the vertical axis that hit our line graph more than once. You can see in the figure below that the dotted line hits our line graph in two places. These are at the points above 2 pm and 5 pm.

We can conclude then that the same number of cars (in particular, 7 cars) was parked outside the school at both 2 pm and 5 pm.

Note that, using our results from the line graph in this example, we can interpret the data as follows: As we might expect, the highest number of cars was parked outside the school at 3 pm, which coincides with when classes end for the day. At 2 pm and 5 pm, we have the same number of cars (7). These may be the teachers’ cars, since by 6 pm almost all of these cars will have also gone, and by this time we would expect both the students and most of the staff to have left for the day.

### Key Points

A line graph is a graph that uses points connected by lines to show how something changes, often, over time.

A line graph will have the following features:

• A horizontal axis across the bottom showing the variable values (often points in time) that we plot information about.
• A vertical axis up the side with a scale for how much or how many.
• A dot or cross on the graph above each variable (or time) point in line with how much or how many on the side axis.
• A line joining each two consecutive points or crosses on the graph. Remember that
• a line going up from left to right between two points means there is an increase in how much or how many.
• a line going down from left to right between two points means there is a decrease in how much or how many.

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