Line Graphs

Line graphs plot values over a continuous axis (usually time), so they excel at showing TRENDS and rates of change. Placement DI uses them for growth, decline and comparison of series.

Method

• Read the axes and units; each point is a value at that x.
• A rising line means increase, falling means decrease; the STEEPER the slope, the faster the change.
• Multiple lines compare series — note where they cross (equal values) and the gap between them.

Feature	Meaning
Upward slope	value increasing
Steeper slope	faster rate of change
Two lines crossing	equal values at that point
Gap between lines	difference of the two series

Example: a series going 100 → 130 over one interval rose 30, i.e. 30% growth; a flat segment means no change. ✓

Exam Tricks & Tips

• 🎯 Steepness = rate of change; the steepest segment is the fastest growth/decline.
• 🎯 A crossing point means the two series are equal there.
• 🎯 The vertical gap between two lines is their difference at that x.
• 🎯 Percentage change between two points uses the earlier point as the base.
• 🎯 A flat (horizontal) segment means the value stayed constant.
• ❌ Don't read a high POINT as high growth — growth is about the slope, not the level.

Expected exam pattern: trend/greatest-increase questions, difference between two series, and percentage change between points. 3 to 5 questions, ~50 seconds each.

Quick recap: points are values, slope is the rate of change, crossings mean equality, and vertical gaps are differences; base percentage change on the earlier point.

Q1. What does a line graph best show?
A1. Trends and rates of change over a continuous axis.

Q2. A steeper slope means?
A2. A faster rate of change.

Q3. Two lines crossing indicates?
A3. The two series are equal at that point.

Q4. The vertical gap between two lines is?
A4. Their difference at that x-value.

Q5. A flat segment means?
A5. The value stayed constant.

Q6. Series rising 100 → 130 — percentage growth?
A6. 30/100 = 30%.

Q7. Base for percentage change between two points?
A7. The earlier point.

Q8. Does a high point mean high growth?
A8. No — growth is about the slope, not the level.

Q9. Downward slope means?
A9. The value is decreasing.

Q10. How to find the fastest growth segment?
A10. Find the steepest upward slope.

Q11. What does each plotted point give?
A11. The value at that x position.

Q12. Multiple lines let you compare?
A12. Different series against each other.

Line graphs show a quantity changing over time, so beyond reading values they test trends — where a quantity rises fastest, peaks, or where two lines cross. Reading slope and intersection is the extra skill here.

What this topic tests: reading time-series values, computing changes and trends, and comparing two or more lines.

The method

Beginner — read points and note the scale

Each point is a value at a time. Note the axis scale and read the required points. As with bars, jotting the values down turns the graph into a table.

Intermediate — trend and rate of change

• Steepest rise/fall = the segment with the greatest slope (change per unit time). "In which year was the increase largest?" is answered by the biggest jump between consecutive points, not the highest point.
• Peak/trough = the highest/lowest point on the line.
• Percentage change between years = (later − earlier)/earlier × 100.

Advanced — multiple lines and intersections

• Two lines let you compare quantities or find where one overtakes the other — the intersection is where they are equal.
• Difference between lines at a point = vertical gap; the maximum gap is where the lines are farthest apart vertically.
• For "combined total", add the two lines' values at each time.

Worked example

A line graph shows a startup's users (in thousands): 2020 = 20, 2021 = 35, 2022 = 40, 2023 = 60. In which year was the growth rate highest?
Yearly growth: 2021 = 15/20 = 75%; 2022 = 5/35 ≈ 14%; 2023 = 20/40 = 50%. The highest growth rate was in 2021 (75%), even though the largest absolute jump was 2023 — read the question (rate vs absolute) carefully.

Where it appears

TCS NQT, Infosys, Wipro, Cognizant, Capgemini DI; line graphs are common for revenue/user/production trends.

Speed tricks and shortcuts

• Largest increase = steepest segment, not the highest point.
• Distinguish absolute change (difference) from growth rate (percentage).
• Intersection of two lines = equal values; vertical gap = difference.
• Mnemonic: "Slope shows the change; the peak shows the level."

Key formulas

• Trend from the slope: rising, falling or flat between points.
• Change = later value − earlier value; growth% = change/earlier ×100.
• Steepest segment = largest rate of change.
• Average over a period = sum of values/number of points.
• Intersection of two lines = equal values.

Usage: read the slope to spot the period of fastest increase or decrease.

Worked Example

Problem: A line graph plots a company's quarterly profit (in ₹ lakh).

Quarter	Q1	Q2	Q3	Q4
Profit	20	35	30	50

Between which two consecutive quarters was the percentage increase in profit the highest?

Solution: Check each consecutive segment (only rising segments can be a percentage increase):

• Q1 → Q2: change = +15 on base 20 → 15/20 = 75% increase.
• Q2 → Q3: change = −5 → this is a decrease, not an increase.
• Q3 → Q4: change = +20 on base 30 → 20/30 = 66.7% increase.

Compare the increases: 75% (Q1→Q2) > 66.7% (Q3→Q4).

Answer: The highest percentage increase was between Q1 and Q2 (75%).