What Is a Worked Example of a Line Chart?

Definition: what a worked example means for a line chart

A line chart is a chart that displays a series of values by plotting points on a horizontal axis (x-axis) and a vertical axis (y-axis), then connecting the points with straight line segments. A “worked example” means you see an explicit, step-by-step scenario where you start from raw values, state every assumption (axis units, point order, how values map to coordinates), and then compute the plotted coordinates and what the chart would visually show.

This matters because the same visual shape can come from different assumptions (for example, whether the x-axis spacing is uniform, whether points are missing, or whether the y-axis uses a transformed scale). A worked example keeps those choices visible so you can verify the result.

Mechanism: how the chart is created (inputs, mapping, and connection)

A line chart requires a sequence of (x, y) pairs.

Inputs

x-values: the horizontal positions. Often they represent time (days, minutes, etc.), but they can represent any ordering variable.
y-values: the measured or computed quantity you want to visualize.

Assumptions you must state

Ordering: the points are plotted in the intended x-order. If you accidentally swap the order, the connecting lines can show a different pattern.
Mapping: each y-value corresponds directly to a vertical coordinate using the chart’s y-axis scale. If you use a non-linear scale (like logarithmic), you must state it.
Missing data: if a data point is missing, you must decide whether to omit the point, interpolate, or break the line. Each choice changes the appearance.
Connection rule: typical line charts connect adjacent points with straight segments. Some systems also support smoothing; smoothing changes geometry and can hide abrupt changes.

What the connections imply The connected segments visually suggest change between observed x-positions. However, the chart does not prove what happened “between” points; it only connects observed values using your connection rule.

Worked example (numerical): plotting explicit coordinates and reading the shape

Assumptions (stated up front):

We use x as day numbers: Day 1 to Day 5.
We use y as an index value measured at the end of each day.
There is no missing data.
The chart connects each day’s point to the next with straight line segments.

Suppose the recorded index values are:

Day 1: y = 100
Day 2: y = 102
Day 3: y = 99
Day 4: y = 105
Day 5: y = 103

Step 1: build the (x, y) pairs

(1, 100)
(2, 102)
(3, 99)
(4, 105)
(5, 103)

Step 2: compute the plotted segments Each segment is the straight line between consecutive points:

From (1, 100) to (2, 102)
From (2, 102) to (3, 99)
From (3, 99) to (4, 105)
From (4, 105) to (5, 103)

Step 3: read the visual change (without assuming hidden information)

The line rises from Day 1 to Day 2.
It drops from Day 2 to Day 3.
It rises more sharply from Day 3 to Day 4.
It falls slightly from Day 4 to Day 5.

Independent verification idea If you recreate the chart, you should place points at exactly those x and y values and connect them in that order. If your chart shows a different direction, it usually means an assumption was different (for example, points were out of order, y-values were transformed, or the x-axis units were changed).

Limitations and risks: at least one failure mode you can check

Missing data or different interpolation If one day’s y-value is missing and your tool interpolates, the line can look smoother than reality. A common failure mode is a gap that is silently filled.
Axis scaling and transformations If the y-axis is transformed (for example, log scale) or uses different units than you think, the same underlying raw values can produce a visually different pattern.
Resolution and aggregation effects If values are averages over a period, the line can conceal intra-period swings. Two time series can look similar at daily resolution but differ at intraday resolution.
Outcomes do not extend between points Even with “daily” x-values, connecting points does not confirm what happened between days. The straight segments are a display rule, not a model of continuous behavior.