DI — Line Graphs

Line graphs plot a value against a continuum (usually time), so they are built to show trends, slopes, and turning points. CAT uses single and multiple lines; the skill is reading not just points but the rate of change between them. Part of the ~22-question DILR block.

What a line encodes

• Point value: y-coordinate at an x (read off the axis).
• Trend: rising, falling, flat across the range.
• Slope: steeper segment = faster change.
• Intersection: two lines cross where their values are equal.

Core operations

Question type	How to answer
Value at a point	Read y off the axis
Change between two points	later − earlier (absolute); ÷ earlier ×100 (%)
Fastest growth	Steepest upward segment (largest %)
Two series compared	Gap = vertical distance; equal where lines cross

Method

1. Read axis scale and units; check even spacing of x-values.
2. For trend questions, scan slope direction, not individual points.
3. For "maximum increase", compare segment steepness / % change, not endpoint height.
4. For multi-line, use the legend and track vertical gaps for "difference" questions.

Exam Tricks & Tips

• 🎯 Steepest slope = largest change, but confirm whether the question wants absolute or percentage change (a steep drop on a big base can be a small %).
• 🎯 Lines crossing = equal values — the go-to for "in which year were X and Y equal?".
• 🎯 The widest vertical gap answers "greatest difference between the two series".
• 🎯 A falling line can still be positive — direction (trend) and sign (value) are different questions.
• 🎯 Percentage change needs the base year; the same absolute rise is a bigger % off a smaller starting value.
• ❌ Common mistake: equating the highest point with the biggest growth — growth is about the change between points, i.e. the slope, not the peak.

Expected exam pattern

0–2 line-graph sets in DILR, single or multiple lines, often paired with a table. Questions: point value, absolute/percentage change, fastest-growth year, equality (crossings), and gap comparisons. MCQ + TITA.

Quick recap

Read lines for trend and slope, not just points. Steepest segment = fastest change (check absolute vs %), crossings = equal values, widest vertical gap = biggest difference. Always anchor percentage change to the correct base.

Cover the answer, recall, then check. 12 cards on line-graph DI.

Q1. What are line graphs best at showing?
A1. Trends, slopes, and turning points over a continuum (usually time).

Q2. What does a steeper segment mean?
A2. A faster rate of change between those two points.

Q3. Where do two lines being equal show up?
A3. At their intersection (crossing) point.

Q4. What answers "greatest difference between two series"?
A4. The widest vertical gap between the lines.

Q5. Absolute vs percentage change — why does it matter for "fastest growth"?
A5. A steep drop/rise on a big base can be a small %; confirm which the question wants.

Q6. Percentage change formula?
A6. ((later − earlier) ÷ earlier) × 100 — earlier value is the base.

Q7. Does a falling line mean a negative value?
A7. No — direction (trend) and sign (value) are different; a falling line can still be positive.

Q8. How do you answer "value at a point"?
A8. Read the y-coordinate off the axis at that x.

Q9. The classic trap in line graphs?
A9. Equating the highest point with the biggest growth — growth is the slope, not the peak.

Q10. How do you compare two series over the range?
A10. Track the vertical gap; use the legend to keep series straight.

Q11. For multi-line graphs, what is load-bearing?
A11. The legend — confirm which line each question refers to.

Q12. How many line-graph sets in CAT DILR?
A12. Typically 0–2, often paired with a table.

Line graphs are built for trends over a continuous variable — usually time. Where bar charts shout "which is bigger", line graphs whisper "which is rising fastest, where do two series cross, when did the trend reverse". CAT questions on line graphs lean on slope (rate of change), intersections, and cumulative vs period reading — all things you extract from the line's shape, not just its points.

What this tests

Trend analysis — reading rate of change (slope), spotting crossovers and turning points, and distinguishing a value at a point from the change between points.

The method

Beginner — read points and axes precisely

Each plotted point is (x-value, y-value). Note the units and scale and whether multiple lines share one axis or use a secondary axis (dual-axis graphs are a trap — a line "above" another may be on a different scale). Read individual values against gridlines as with bars.

Intermediate — slope means rate of change

The steepness of a segment = how fast the quantity changed over that interval. For "in which period did sales grow fastest", find the steepest upward segment, not the highest point. A line can be high but flat (large value, no growth) or low but steep (small value, rapid growth). Separate level (where the line is) from change (how tilted it is).

Advanced — the FAST CAT approach: exploit crossings, gaps, and reversals

• Intersection of two lines = the point where the two quantities are equal; questions like "when did exports overtake imports" are answered at the crossover.
• Vertical gap between two lines at any x = the difference between the quantities there; the widest gap = maximum difference. You can read differences by eye without computing both values.
• Turning point (peak/trough) = where a trend reverses; "when did growth turn to decline" is the local maximum.
• For cumulative line graphs, the period value = current point − previous point (like stacked bars over time).

Answer slope/gap/crossover questions visually first, compute only to break ties.

Worked example

Two lines show a firm's Revenue and Cost (₹ crore) over Years 1–5. Revenue: 50, 70, 90, 110, 130. Cost: 40, 65, 85, 95, 100.
Question: In which year was profit (Revenue − Cost) the highest?
Profit = vertical gap between the lines:

• Y1: 10, Y2: 5, Y3: 5, Y4: 15, Y5: 30.
  The gap is widest in Year 5. You could read this straight off the graph — the lines diverge most at the right end. Answer: Year 5. Note the trap: revenue is highest in Y5 and profit is highest in Y5 here, but in many problems the highest-revenue year is not the highest-profit year, because cost matters. Always read the gap, not one line.

CAT relevance

Line graphs recur in DI sets and pair naturally with bar/table data in multi-source sets. Their signature questions — fastest growth, crossover year, maximum difference — are visually solvable, giving a speed edge if you read slope and gaps directly instead of tabulating every value.

Speed tricks & shortcuts

• Steepest segment = fastest change; don't confuse it with the highest point.
• Line crossing = equality of the two quantities.
• Vertical gap = difference; widest gap = max difference (read by eye).
• Watch for a secondary axis — lines may be on different scales.
• Mnemonic — "Slope for speed, gap for difference, cross for equal."

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 startup's monthly active users (MAU, in lakh) over five months:
Jan 10, Feb 15, Mar 18, Apr 27, May 30.
(a) In which month was the month-on-month percentage growth highest? (b) What was the average monthly growth in users (absolute) over the period?

Solution:
Line graphs show a trend over time; the slope between two points is the change, and month-on-month percentage growth = (this month − last month)/last month × 100. Compute each interval:

• Feb: (15 − 10)/10 = 5/10 = 50%
• Mar: (18 − 15)/15 = 3/15 = 20%
• Apr: (27 − 18)/18 = 9/18 = 50%
• May: (30 − 27)/27 = 3/27 ≈ 11.1%

(a) Highest percentage growth: Feb and Apr are TIED at 50%. Note that Apr had the largest absolute jump (9 lakh, the steepest line segment), but its percentage (9/18 = 50%) equals Feb's (5/10 = 50%) because Feb grew from a smaller base. If the question wants a single month by percentage, it is a tie at 50% (Feb and Apr); the steepest SLOPE (absolute rise) is April. This slope-vs-percentage distinction is a classic line-graph trap.

(b) Average monthly growth (absolute) = total increase / number of intervals.
Total increase over the period = May − Jan = 30 − 10 = 20 lakh.
Number of intervals (Jan→Feb→Mar→Apr→May) = 4.
Average monthly growth = 20 / 4 = 5 lakh per month.
(Equivalently, average the four monthly increases: (5 + 3 + 9 + 3)/4 = 20/4 = 5.)

Answer: (a) Highest month-on-month PERCENTAGE growth is a tie at 50% (February and April); April alone has the steepest absolute rise (9 lakh). (b) Average absolute monthly growth = (30 − 10)/4 = 5 lakh per month.