A line graph shows how a value changes over time.
This lesson shows how to read it, then gives each rule with the reason it works. It solves five examples step by step and lists the traps that cost marks.
- Read: year across, value up.
- Average: total ÷ count.
- Difference: bigger − smaller.
- Percentage: (first ÷ second) × 100.
- Increase %: change ÷ old × 100.
What a Line Graph Shows
What is a line graph?
A line graph joins points with straight lines. Each point is one value at one moment.
The sideways axis usually shows time, such as years. The upright axis shows the amount.
It is built to show how something changes over time.
How do I read a value?
Find the year on the sideways axis. Go up to the point. Then read across to the upright axis.
Always check the units first. They may be thousands, lakh tonnes or crore rupees.
When a graph has many lines, find the right line first. Then read it.
What does the shape of the line tell me?
A line going up means the value grew. A line going down means it fell.
A steeper line means a faster change.
A flat line means no change.
The highest point of the line is the peak. The lowest is the dip.
How is a line graph different from a bar graph?
A bar graph compares separate groups at one time. A line graph follows one thing as time passes.
A line is best when the order of the points matters, such as years.
Use bars for “which is biggest”. Use a line for “how did it change”.
Check 1
A steeper line on a line graph means a faster change.
Core Rules and Why They Work
How do I find a total or an average?
Total = add all the values. Average = total ÷ number of values.
Why it works: the average is the value each point would have if all were equal. Sharing the total equally gives it.
How do I find a difference or a ratio?
Difference = bigger − smaller. Ratio = first value : second value, cut down by their H.C.F.
Why it works: a difference counts how far apart two points are. A ratio compares their sizes without units.
How do I find a percentage or a percentage change?
One value as a percentage of another = (first ÷ second) × 100.Percentage increase = (new − old) ÷ old × 100.
Why it works: percent means out of 100. The change is always measured against the old value.
How do I compare two lines in the same year?
Read both lines at the same year. Then subtract or divide.
Where two lines cross, the two values are equal at that moment.
Check 2
To find a percentage increase, divide the change by the new value.
Five Solved Examples
Easy, step by step: Shimla had 207, 359, 114, 372 and 365 thousand tourists in five years. Find the total.
Step 1: write the five values.
Step 2: 207 + 359 = 566. Then 566 + 114 = 680.
Step 3: 680 + 372 = 1052. Then 1052 + 365 = 1417.
The total is 1417.
Easy, step by step: Self-Help books sold total 614 over 5 quarters. Find the average.
Step 1: average = total ÷ count.
Step 2: 614 ÷ 5 = 122.8.
The average is 122.8.
Medium, step by step: in 2018 Udaipur had 43 and Shimla had 359. Find the difference.
Step 1: pick the bigger value, 359.
Step 2: 359 − 43 = 316.
The difference is 316.
Medium, step by step: Manali had 106 and Udaipur had 186 in 2022. Manali is what percentage of Udaipur?
Step 1: percentage = (106 ÷ 186) × 100.
Step 2: 106 ÷ 186 = 0.5699.
Step 3: 0.5699 × 100 = 56.99, which rounds to 57%.
Exam level, step by step: Cotton exports were 35 in 2017 and 133 in 2018. Find the percentage increase.
Step 1: change = 133 − 35 = 98.
Step 2: divide by the old value. 98 ÷ 35 = 2.8.
Step 3: 2.8 × 100 = 280.
The increase is 280%.
Exam level, step by step: in 2019 Udaipur had 267 and Shimla had 114. Find the ratio of Udaipur to Shimla.
Step 1: write the ratio 267 : 114.
Step 2: find the H.C.F. Both numbers divide by 3. 267 ÷ 3 = 89 and 114 ÷ 3 = 38.
Step 3: 89 and 38 share no more factors.
The ratio is 89 : 38.
Check: 89 × 114 and 38 × 267 both equal 10146.
Exam level, step by step: in 2018 the five places had 43, 359, 183, 293 and 152 thousand tourists. Which had the most, and what is the average?
Step 1: scan the values. 359 is the biggest, so Shimla had the most.
Step 2: add them. 43 + 359 = 402. Then 402 + 183 = 585.
Step 3: 585 + 293 = 878. Then 878 + 152 = 1030.
Step 4: average = 1030 ÷ 5 = 206.
Shimla led, and the average was 206 thousand.
Check 3
Udaipur 43 and Shimla 359 in 2018 give a difference of 316.
Common Traps and Shortcuts
Which traps cost marks?
Reading the wrong line when the graph has many.
Ignoring the units, such as thousands or lakh tonnes.
Dividing by the new value when finding a percentage increase.
Reading a point just above or below the right year.
Mixing up “difference” with “ratio”.
Which shortcuts save time?
For “highest” or “lowest”, scan the line for its peak or dip. No sums are needed.
For a ratio, cut by the H.C.F. only at the end.
For a percentage, estimate first. Then match the nearest option.
For an average of five values, add and then divide by 5.
What patterns come up in exams?
Six types repeat. Highest year, highest category, total, average, difference and ratio.
Percentage of another value and percentage increase come up too.
Each one needs only two or three values read from the graph.
What should I do before I start any question?
Read the title of the graph and the units.
Read the question twice. Note the year or the line it asks about.
Write the values you read in a short list.
Then do the sum on paper, not in your head.
Last, check that your answer is the right size by estimating.
Check 4
For a highest-value question, you must add all the values first.
MCQ on Line Graphs
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