DILR Line Graph and Trend Sets: Read the Slope, Not Value

DILR

A line graph looks easy because you can see it. The trouble starts with the questions. Which year had the highest growth? In which period did two companies move in opposite directions? When was the gap between them the widest? The eye is drawn to the highest point on the graph, and that is often the wrong thing to look at.

This guide shows how to read a line graph by its slope, the steepness of each segment, because most questions are about change and not level. You will see how to compare slopes between two lines, how to convert a slope into a growth rate, and where the usual traps are. The numbers in the examples are invented for illustration and were all checked by calculation.

Why the Eye Goes to the Wrong Place

The highest point on a line graph draws attention, and many questions are designed to use that. A question may ask in which year sales grew the most, and the tempting answer is the year with the highest sales. That is a level, not a change. The year with the highest growth might be an early one where the line rose steeply from a low base.

There are two quantities hidden in any line graph. The level is the value at a point. The change is the difference between two points. Questions on growth, decline, rate of change, and turning points all depend on the second.

Slope is the picture of change. A rising segment is positive change, a falling segment is negative, and the steeper it is, the greater the change per unit of time. Learning to read the steepness is the first skill, and it takes only a little practice.

Slope Gives Absolute Change

Take Company A with values 100, 120, 150 and 160 over four consecutive years. The change from year 1 to year 2 is 20, from year 2 to year 3 is 30, and from year 3 to year 4 is 10. The segment from year 2 to year 3 is the steepest, and the segment from year 3 to year 4 is the flattest, though the line is still rising.

This is where a common mistake appears. A question asks when sales fell, and you look for a falling segment. In this case the line never falls. It only rises more slowly at the end. Slower growth is not a decline. Read the direction of the segment before you read its steepness.

For a set with many points, make a short row of changes beneath the graph, written as plus 20, plus 30, plus 10. This takes ten seconds and turns every later question on absolute change into a lookup. It is one of the best uses of the first minute of a line graph set.

Period	Company A change	Company A growth rate	Company B change
Year 1 to 2	Plus 20	20 percent	Plus 10
Year 2 to 3	Plus 30	25 percent	Plus 20
Year 3 to 4	Plus 10	About 6.7 percent	Plus 30

Slope Does Not Give Percentage Growth

Percentage growth is the change divided by the starting value, so it depends on where the segment starts. For Company A, the change from year 2 to 3 is 30 on a base of 120, which is 25 percent. The change from year 1 to 2 is 20 on a base of 100, which is 20 percent. The steeper segment also has the higher rate, here, but that is not guaranteed.

Consider the last period. The change of 10 on a base of 150 is only about 6.7 percent. If another company had a rise of 10 on a base of 50, the change would be 20 percent. Two segments with the same slope can have very different growth rates, depending on the base.

So the rule is: slope answers absolute change questions, and slope with the base answers percentage questions. When a question uses the word percent, rate or growth, check the starting value. Our guide on percentage change, growth and CAGR traps covers the typical errors in the arithmetic.

Comparing Two Lines

Many sets plot two or more lines on one graph. Questions then compare them: which line grew faster, when did they diverge, and when was the gap widest. Compare the slopes segment by segment. Where one line is steeper in the same direction, the gap between them widens. Where the other is steeper, the gap narrows.

Look at the example, and suppose Company B has values 200, 210, 230 and 260. Company B rises by 10, 20 and 30 over the three periods, against 20, 30 and 10 for Company A. B starts above A, so the gap B minus A is 100, then 90, then 80, then 100. In the first two periods A grows faster, so the gap narrows. In the third period B rises by 30 while A rises by 10, so the gap widens again. The widest gap is 100, and it occurs in both the first and the last year.

That is the second trap. The gap between two lines depends on both their levels and their slopes. A line can be steeper and still be below the other. To find when the two cross, look for the point where the faster rising line catches up. You will often need the actual values, and not only the shape.

Reading the Axes and the Scales

Check the axes before the lines. If the vertical axis does not start at zero, the picture exaggerates changes. If two graphs in a set use different scales, a steep line in one is not comparable to a steep line in the other. Compare numbers, not appearance.

Look also at the units. A graph may show a value in thousands for one line and in lakhs for another. A question that asks you to compare them will test whether you converted. Another version has two vertical axes, one on each side, with each line tied to one of them. Reading a point against the wrong axis is a typical slip.

For years on the horizontal axis, check whether they are consecutive. Some graphs skip years, and the slope between two points that are three years apart is a change over three years, not one. Dividing by the number of years gives the average per year. Our guide on reading combination charts shows how to handle graphs that combine lines and bars.

Turning Points and Crossovers

A turning point is where the direction of a line changes, from rising to falling or the reverse. Questions often ask for the year of a peak or a trough, and the answer is the point at which the sign of the change flips. The change row shows it immediately: a run of positive numbers followed by a negative one puts the peak at the last point before the negative.

A crossover is where two lines meet. Before the crossover one line is above the other, and after it the order is reversed. To find the crossover between plotted points, you need the actual values, and a question that asks for it in a period between two years may say to assume a straight line change. Without that assumption, the best you can say is that the crossover happened within the period.

Both ideas are quick to find from the change row and the values, and both are frequent in questions. Mark them on the graph with a small symbol as you read, so that you do not search again for each question.

What the Graph Does Not Tell You

A line graph connects plotted points with straight segments. The values between the points are not data. If a question asks for the value halfway through a period, the graph cannot answer it, unless the question says to assume a steady change. Be careful with questions that ask what happened in a month when the points are yearly.

The graph also does not say why the change happened. A question may offer an option that explains the rise with a cause. If the set has no information on causes, that option is not supported, however sensible it sounds.

Finally, the graph shows trends, but a question about the future asks for an assumption. If the set says to assume the trend continues, then extend the slope. If it does not, the correct answer is often that it cannot be determined.

Fit slope practice into your week with the CAT study planner, and if you want feedback on how you handle DI sets, you can talk to a CAT mentor.