A good graph has a sensible scale, labelled axes with units, accurately plotted points, a best-fit line and, when needed, a gradient taken from a large triangle.
This lesson is part of SPM Physics measurement. It uses readings from reading measuring instruments and uncertainty.
What is the order of steps?
Follow the same order each time.
- Choose the axes: the variable you change goes on the horizontal axis.
- Choose a scale: points should fill more than half the paper, in steps of 1, 2 or 5.
- Label each axis with the quantity and unit.
- Plot each point exactly, with a clear mark.
- Draw a best-fit line and calculate the gradient.
Worked example: a spring
An original experiment: a force is applied to a spring, and the extension is measured.
| Force F (N) | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 |
|---|---|---|---|---|---|
| Extension x (cm) | 2.1 | 3.9 | 6.2 | 7.9 | 10.1 |
The student changes the force, so force goes on the horizontal axis and extension on the vertical axis. Extension runs to 10.1 cm, so a scale of 1 cm of paper for every 1 cm extension fits a 12 cm axis. Force runs to 5.0 N, so 2 cm of paper for every 1 N fills 10 cm.
The points lie close to a straight line through the origin. Draw one line with roughly equal numbers of points above and below it, not a line joining each dot.
How do you find the gradient?
Suppose the line passes through (1.0, 2.0) and (5.0, 10.0). Choose two points far apart.
Gradient = (10.0 − 2.0) ÷ (5.0 − 1.0) = 8.0 ÷ 4.0 = 2.0 cm/N.
This means the spring extends 2.0 cm for every newton, and the force per unit extension is the reciprocal, 0.50 N/cm.
The mistakes that cost marks
| Part of the graph | Wrong | Right |
|---|---|---|
| Scale | 3 squares = 1 cm, points crowded in a corner | 2 squares = 1 cm, points fill the paper |
| Axis label | “Extension” with no unit | “Extension, x / cm” |
| Line | Joins every dot | One smooth best-fit line |
| Gradient triangle | Small, using two data points | Large, using points on the line |
The gradient has a unit as well. Leaving out cm/N loses the mark, even when the number is right.
Check yourself
Choose a scale for a horizontal axis that must show time from 0 s to 48 s on graph paper 18 cm wide. Then say why 1 cm for 3 s, although it fits, is a poor choice.
Answer
A scale of 1 cm for 2 s needs 24 cm, which is wider than the paper. A scale of 1 cm for 4 s needs 12 cm and fills two-thirds of the paper, so it is a good choice.
A scale of 1 cm for 3 s would fit (16 cm), but steps of 3 make plotting and reading harder and cause errors. Steps of 1, 2, 4 or 5 are easier to use.
What to study next
Continue with the measurement practice set, which includes a plotting question. The graph evidence and fair-comparison lab helps you practise choosing lines.
If you want a teacher to check a graph you drew, see online one-to-one Physics tuition.