Line Graphs
A line graph displays data using points connected by straight lines. It is especially useful for showing how data changes over time — for example, temperature during a day, a student's marks over months, or the growth of a plant.
In Class 5, you learn to read, interpret, and draw line graphs. Line graphs help you identify trends — whether values are increasing, decreasing, or staying the same.
Unlike bar graphs that compare different categories, line graphs show continuous data and help us predict future values based on the pattern.
What is Line Graphs - Class 5 Maths (Data Handling)?
A line graph is a graph where data points are plotted and connected by straight line segments. It shows how a quantity changes over equal intervals of time or other continuous scale.
Parts of a line graph:
- Title — describes what the graph shows
- X-axis (horizontal) — shows time periods or continuous categories
- Y-axis (vertical) — shows values (numbers/quantities)
- Data points — dots plotted at exact positions
- Line segments — straight lines connecting consecutive data points
Types and Properties
Patterns in Line Graphs:
- Rising line (upward trend): Values are increasing. Example: price of goods over years.
- Falling line (downward trend): Values are decreasing. Example: stock of rice over a week.
- Flat line (no change): Values stay the same over time.
- Zigzag pattern: Values go up and down. Example: daily temperature over a week.
Solved Examples
Example 1: Example 1: Reading a Line Graph
Problem: The line graph shows the temperature of a city over 5 days:
| Day | Temperature (°C) |
|---|---|
| Monday | 28 |
| Tuesday | 30 |
| Wednesday | 32 |
| Thursday | 29 |
| Friday | 31 |
(a) On which day was the temperature highest? (b) Between which two days did the temperature drop?
Solution:
(a) Wednesday had the highest temperature: 32°C.
(b) The temperature dropped between Wednesday (32°C) and Thursday (29°C).
Answer: (a) Wednesday (b) Wednesday to Thursday
Example 2: Example 2: Finding the Change
Problem: The line graph shows Ria's savings (in ₹) over 4 months: Jan = ₹200, Feb = ₹350, Mar = ₹300, Apr = ₹500. How much more did she save in April than in January?
Solution:
Step 1: Difference = ₹500 − ₹200 = ₹300
Answer: Ria saved ₹300 more in April than in January.
Example 3: Example 3: Identifying a Trend
Problem: A line graph shows plant height over 5 weeks: Week 1 = 3 cm, Week 2 = 5 cm, Week 3 = 8 cm, Week 4 = 12 cm, Week 5 = 17 cm. What is the trend?
Solution:
Step 1: The values increase every week: 3, 5, 8, 12, 17.
Step 2: The line goes upward throughout.
Answer: The trend is continuously increasing. The plant grew taller each week.
Example 4: Example 4: Drawing a Line Graph
Problem: Draw a line graph for Aman's test scores over 5 months: Aug = 65, Sep = 70, Oct = 80, Nov = 75, Dec = 90.
Solution:
Step 1: Draw X-axis (months) and Y-axis (marks). Scale: 1 division = 10 marks.
Step 2: Plot points: (Aug, 65), (Sep, 70), (Oct, 80), (Nov, 75), (Dec, 90).
Step 3: Connect consecutive points with straight lines.
Step 4: Add title: "Aman's Test Scores".
Answer: The line graph shows an overall upward trend with a slight dip in November.
Example 5: Example 5: Predicting from a Line Graph
Problem: A shop's monthly sales (in units) are: Jan = 100, Feb = 120, Mar = 140, Apr = 160. If the pattern continues, what might May's sales be?
Solution:
Step 1: The increase each month = 20 units.
Step 2: Predicted May sales = 160 + 20 = 180 units.
Answer: May's sales are likely to be around 180 units.
Example 6: Example 6: Maximum and Minimum
Problem: The line graph shows visitors to a park over a week: Mon = 50, Tue = 40, Wed = 60, Thu = 45, Fri = 70, Sat = 120, Sun = 110. Find the difference between the maximum and minimum visitors.
Solution:
Step 1: Maximum = Saturday: 120 visitors
Step 2: Minimum = Tuesday: 40 visitors
Step 3: Difference = 120 − 40 = 80
Answer: Difference = 80 visitors
Example 7: Example 7: Rate of Change
Problem: Priya's height over 4 years: Age 8 = 120 cm, Age 9 = 125 cm, Age 10 = 132 cm, Age 11 = 140 cm. In which year did she grow the most?
Solution:
Step 1: Growth from 8 to 9 = 125 − 120 = 5 cm
Step 2: Growth from 9 to 10 = 132 − 125 = 7 cm
Step 3: Growth from 10 to 11 = 140 − 132 = 8 cm
Answer: Priya grew the most between age 10 and 11 (8 cm).
Example 8: Example 8: Total from Line Graph
Problem: A line graph shows books sold each month: Jan = 30, Feb = 45, Mar = 25, Apr = 50. Find the total books sold.
Solution:
Step 1: Total = 30 + 45 + 25 + 50 = 150
Answer: Total books sold = 150
Example 9: Example 9: Comparing Two Line Graphs
Problem: The line graph shows runs scored by Kavi and Dev over 4 matches:
| Match | Kavi | Dev |
|---|---|---|
| 1 | 30 | 45 |
| 2 | 50 | 40 |
| 3 | 45 | 55 |
| 4 | 60 | 50 |
In how many matches did Kavi score more than Dev?
Solution:
Step 1: Match 1: Dev more. Match 2: Kavi more. Match 3: Dev more. Match 4: Kavi more.
Answer: Kavi scored more in 2 matches (Match 2 and Match 4).
Key Points to Remember
- A line graph connects data points with straight line segments.
- It is best for showing change over time.
- Rising line = values increasing; Falling line = values decreasing.
- The steeper the line, the faster the change.
- Two line graphs on the same axes can be used to compare two data sets.
- Line graphs can help predict future values if a pattern exists.
- Always label both axes and give the graph a title.
Practice Problems
- A line graph shows the price of mangoes (per kg) over 4 months: May = ₹80, June = ₹60, July = ₹50, Aug = ₹70. In which month were mangoes cheapest?
- Draw a line graph for the number of students absent each day: Mon = 3, Tue = 5, Wed = 2, Thu = 4, Fri = 1.
- A line graph shows a plant's height: Week 1 = 4 cm, Week 2 = 7 cm, Week 3 = 11 cm, Week 4 = 16 cm. How much did the plant grow from Week 2 to Week 4?
- Aditi scored 70, 75, 65, 80, 85 in five monthly tests. What is the overall trend?
- From a line graph, the highest value is 95 and the lowest is 40. What is the range?
- Two line graphs show rainfall in Delhi and Mumbai over 4 months. In how many months is Delhi's rainfall greater?
Frequently Asked Questions
Q1. What is a line graph used for?
A line graph is used to show how data changes over time. It displays trends such as increase, decrease, or no change in a clear visual way.
Q2. How is a line graph different from a bar graph?
A bar graph uses rectangular bars to compare different categories. A line graph connects data points with lines to show changes over time. Line graphs show trends; bar graphs compare quantities.
Q3. What does a steep line on a line graph mean?
A steep (sharply sloping) line means the value is changing rapidly. A gentle slope means the value is changing slowly.
Q4. Can a line graph show more than one data set?
Yes. You can plot two or more lines on the same graph using different colours or styles. This makes it easy to compare trends between data sets.
Q5. How do you draw a line graph?
Draw X and Y axes, choose a scale, plot each data point as a dot at the correct position, connect the dots with straight lines, and add a title and labels.
Q6. What is a trend in a line graph?
A trend is the general direction of the data over time. An upward trend means values are mostly increasing. A downward trend means values are mostly decreasing.
Q7. Can we predict future values from a line graph?
If the data shows a clear pattern, you can extend the trend line to estimate future values. This is called extrapolation and gives approximate predictions.
Q8. What is the range in a line graph?
The range is the difference between the highest and lowest values on the graph. It shows how much the data varies.
