Single Line Graphs — Fundamental Concepts

Fundamental Concepts

Four-column working table

Record time, value, change from the previous point and elapsed duration. This is enough for most single-series questions and avoids repeatedly estimating the same coordinates.

Coordinate checks

Read the requested horizontal label exactly.
Calculate the value per grid interval from labelled ticks.
Count spaces between ticks, not boundary lines.
Keep the vertical unit attached to each number.
Treat a missing observation as unknown, not zero.

Interval checks

Later minus earlier gives signed change. Divide by elapsed time for average rate. The greatest level, greatest increase and greatest absolute rate are different quantities. Repeated maxima may require more than one time in the answer.

Interpolation rule

Only assume constant change between points when the question supplies that convention. The fraction of elapsed time determines the fraction of total change. Interpolated values are estimates under a model, not new observations.

Meaning of the axis

A flat tank-volume line can coexist with equal inflow and outflow. A falling distance-from-start line indicates movement closer to the start under the appropriate route interpretation; it is not negative distance. Net change is final minus initial, while total movement may require the sum of interval magnitudes and additional path information.

As a final arithmetic check, add the signed interval changes. They should equal the difference between the final and initial recorded values.