Chapter 10 · Measurement and data
Line Graphs: Read Values, Find Change, Make One
Read values on a line graph, see where the data rise, fall or stay the same, find how much a value changed, and make your own line graph from a table.
A line graph shows how a value changes from one time to the next. You have already read scales on bar graphs. A line graph has the same kind of scale on its vertical axis, the axis that runs up the side. But instead of a bar, it marks each value with a dot.
- The horizontal axis runs across the bottom. It lists the times in order, from left to right. In this lesson, the times are days (Monday to Friday) or weeks (Week 1 to Week 4).
- A point is a dot that shows the value at one time.
- A line segment is the straight piece of line that joins one point to the next one, in time order.
- On every graph in this lesson, the scale starts at 0 and goes up by the same amount each time.
The line graph below shows the highest temperature each day for one week.
To read a value, find the time on the horizontal axis. Go straight up to its point. Then look straight across to the scale.
- If the point is level with a number on the scale, that number is its value.
- If the point is between two numbers, its value is between them. For example, a point halfway between 20 and 30 shows 25.
Read values only at the points. A segment shows which point comes next. It does not show a value between two times.
On this graph, the horizontal axis is labeled Day. The scale is in degrees Fahrenheit, from 0 at the bottom to 80 at the top. Monday's point shows 45 degrees Fahrenheit. Tuesday's and Wednesday's points each show 55 degrees Fahrenheit. Thursday's point shows 70 degrees Fahrenheit. Friday's point shows 60 degrees Fahrenheit.
Worked example
Read the temperature graph
Use the temperature graph above. What temperature does it show for Thursday? Then tell where the temperature rose, fell or stayed the same from Monday to Friday.
Find Thursday on the horizontal axis. Go straight up to its point, then look straight across to the scale. The height of the point is its value, so Thursday's temperature is 70 degrees Fahrenheit.
Next, compare each day with the next day, since each segment joins two days in time order. If the next value is greater, the temperature rose and the segment goes up. If it is less, the temperature fell and the segment goes down. If it is equal, the temperature stayed the same and the segment is flat.
Compare Monday with Tuesday: 55 is greater than 45, so the temperature rose. Compare Tuesday with Wednesday: both are 55, so it stayed the same.
Compare Wednesday with Thursday: 70 is greater than 55, so it rose. Compare Thursday with Friday: 60 is less than 70, so it fell.
Answer
The graph shows 70 degrees Fahrenheit for Thursday. The temperature rose from Monday to Tuesday, stayed the same from Tuesday to Wednesday, rose from Wednesday to Thursday, and fell from Thursday to Friday.
Key concept
How a line graph shows change
Each point on a line graph is one pair: a time and its value. The points are joined in time order, so from one point to the next you can see whether the value rose, fell or stayed the same.
The change between two times is how much the value went up or down. Subtract the smaller value from the greater value. Then say whether it was a rise or a fall, going from the earlier time to the later time. If the two values are equal, there is no change. Only the values at those two times matter: the points in between do not change the answer.
Worked example
Find a change between two times
A class counted how many books they read each week. The line graph above shows 30 books in Week 1, 40 books in Week 2, 50 books in Week 3 and 20 books in Week 4. How much did the number of books change from Week 1 to Week 4?
Find the two times in the question. Week 1's point shows 30 books, and Week 4's point shows 20 books. The change compares only these two times, so these are the two values you need.
Subtract the smaller value from the greater value, because the change is how far apart the two values are. Here 30 is greater than 20.
Decide if it is a rise or a fall. Week 4 is the later time, and its 20 books is less than Week 1's 30 books, so the number fell. The line rises from Week 1 to Week 3 and then falls to Week 4, but the points for Week 2 and Week 3 are in between, so they do not change the answer.
Answer
From Week 1 to Week 4, the number of books the class read fell by 10 books.
Now you will make a line graph from a table. Each row of the table is one pair: a time and its value. Each pair becomes one point. The time tells you where the point goes along the horizontal axis. The value tells you how high to put it.
First, choose a scale for the vertical axis. The scale is your choice, as long as you:
- start at 0,
- pick a step, the amount you count up by, and use the same step every time,
- use enough steps to reach the greatest value in the table.
Your step does not have to fit every value exactly. If a value falls between two numbers on your scale, put its point between them. For example, if you count by 10s, a value of 15 goes halfway between 10 and 20.
The table below shows how many students rode a bike to school each day.
| Day | Students |
|---|---|
Monday | 15 |
Tuesday | 25 |
Wednesday | 20 |
Thursday | 20 |
Friday | 35 |
Worked example
Make a line graph from the table
Make a line graph from the table: 15 students on Monday, 25 students on Tuesday, 20 students on Wednesday, 20 students on Thursday and 35 students on Friday.
Draw the two axes. Write the days in time order, Monday to Friday, along the horizontal axis, and label it Day. Label the vertical axis with the unit, students. The labels tell a reader what the graph shows.
Choose a scale. Start at 0 and count up by 5s. Seven steps of 5 reach 35, the greatest value, so you need at least 7 steps for every point to fit. Eight steps also work, and this graph uses 8, so its scale ends at 40 students. Other steps, such as 10, would work too, as long as there are enough of them to reach 35.
Plot one point for each row, because each row is one pair. Find the day, go up to its value, and draw a dot. Starting from 0, Monday's 15 is 3 steps up, Tuesday's 25 is 5 steps up, Wednesday's and Thursday's 20 are 4 steps up, and Friday's 35 is 7 steps up.
Join each point to the next one with a straight segment, in time order from Monday to Friday. Time order matters because each segment compares one day with the next. Check against the table: the line rises from Monday to Tuesday, falls to Wednesday, stays flat to Thursday and rises to Friday.
Answer
The finished line graph has five points, at 15, 25, 20, 20 and 35 students from Monday to Friday, joined in order by four segments.
Takeaway: A line graph shows one value at each time, with the points joined in time order. Read each value only at its point. To find the change between two times, use just those two values: subtract the smaller from the greater, and call it a rise or a fall from the earlier time to the later one. If the two values are equal, there is no change. To make a line graph, choose a scale that starts at 0 and has enough equal steps to reach the greatest value (a value may sit between two numbers on your scale). Then plot one point for each pair and join the points in time order.
Next, you will build tables and plots from lists of data, and solve problems that combine values read from graphs and tables.