What a line graph is for
Line graphs show how a value changes over time. Each point is a reading; the slope between points shows how fast it changed.
An upward segment is an increase; a downward segment is a decrease.
The steepest segment is the largest change in absolute terms, if the time steps are equal.
Example data
Noon temperature (°C) over a week:
Day | Mon | Tue | Wed | Thu | Fri | Sat | Sun |
|---|---|---|---|---|---|---|---|
°C | 28 | 31 | 30 | 34 | 33 | 36 | 32 |
Day-to-day changes: +3, −1, +4, −1, +3, −4.
The largest single-day rise is Wednesday to Thursday (+4); the largest fall is Saturday to Sunday (−4).
The temperature fell on 3 days: Wednesday, Friday and Sunday.
Average: 224 ÷ 7 = 32 °C; three days (Thu, Fri, Sat) were above it.
Range: 36 − 28 = 8 °C.
Growth rates
Percentage change between two points = (later − earlier) ÷ earlier × 100.
Example. A company's profit (₹ crore): 2019 10, 2020 12, 2021 9, 2022 15, 2023 18.
2022 to 2023: 3/15 = 20% growth.
2020 to 2021: −3/12 = 25% decline.
2023 compared with 2019: 8/10 = 80% higher.
Two lines on one graph
When two series share axes, compare them point by point. Where the lines cross, the two values are equal. The gap between the lines is the difference at each point.
Shortcuts and tricks
The standard way is to list every value and calculate. With the values listed, these shortcuts answer the common questions faster.
Average by deviation
Example: readings of 18, 22, 20, 25 and 15.
Standard way: the total is 100, and 100 ÷ 5 = 20.
Shortcut: take 20 as a base. The deviations −2, +2, 0, +5 and −5 cancel, so the average is 20.
Rises and falls from the changes
Write the change between each pair of points once (+3, −1, +4, …). The largest rise, the largest fall and the number of falling days can then all be read from that one list.
Growth as a fraction
Example: a value goes from 16 to 20.
Standard way: 4 ÷ 16 × 100 = 25%.
Shortcut: 4/16 = 1/4, which is 25%.
Exam tips
Check whether the vertical axis starts at zero; a cut axis makes small changes look large.
"Trend" questions ask about direction over the whole period, not one segment.
List the values first, then answer every question from the list.