Line Graphs — Fundamental Concepts

Fundamental Concepts

Coordinate reading

Identify the ordered horizontal variable and the vertical measure. Read units, time intervals and legend entries before comparing series. A point gives a level; a segment connects observations and suggests their sequence.

Operation map

Level: — read the vertical coordinate at a specified observation.
Absolute change: — later value minus earlier value.
Average rate: — change divided by elapsed time or horizontal distance in the stated unit.
Percentage change: — change divided by the initial value, multiplied by 100.
Gap between series: — compare values at the same horizontal coordinate.
Cumulative addition: — subtract successive cumulative totals.

Interpretation safeguards

The largest level need not follow the fastest growth. Equal absolute increases need not have equal percentage increases. Unequal time intervals require rate calculations. A flat line means unchanged displayed value, not necessarily absence of all activity.

Connecting points

Distinguish a measured observation from an interpolated value. A crossing between points establishes exact equality only under the stated interpolation model. Extrapolation beyond the recorded range requires an additional assumption and should not be presented as observed fact.

Aggregation

Do not add cumulative totals as if they were independent period flows. Do not infer causation from two lines moving together. Record the question type first, then use only the coordinates needed. This prevents correct arithmetic on the wrong quantity and avoids treating missing observations as zero.