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Inverse proportion

Two quantities are inversely proportional when their product is constant, giving a curved graph. Plotting one quantity against the reciprocal of the other straightens it into a line through the origin.

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Inverse proportion describes a relationship where increasing one quantity decreases the other so that their product stays constant. A familiar example is the pressure and volume of a fixed mass of gas at constant temperature: as volume falls, pressure rises, and pressure times volume stays roughly the same.

Plotted directly, an inverse relationship gives a smooth curve, not a straight line, which is harder to analyse. The standard technique is to plot one quantity against the reciprocal of the other. Plotting pressure against one over volume, for instance, turns the curve into a straight line through the origin.

That straightening is powerful because it lets you use the familiar tools of a straight-line graph, reading the gradient as the constant that links the quantities.

Recognising when to use a reciprocal to straighten a curve is a key data-analysis skill, and it shows genuine understanding of the underlying relationship rather than just plotting raw values.

Volume / cm³ Pressure / kPa

What examiners award

Marks are awarded for recognising inverse proportion from a constant product, and for plotting one quantity against the reciprocal of the other to get a straight line through the origin.

Common mark losses

Marks are lost for trying to read a gradient from the curved raw graph, or for confusing inverse proportion with a simple decreasing straight line.

In short

Two quantities are inversely proportional when their product is constant, giving a curved graph. Plotting one quantity against the reciprocal of the other straightens it into a line through the origin.

A routine that works

Practise the mechanics until they are automatic: label both axes with units, choose a scale that fills more than half the grid, plot points with a sharp pencil, draw a single best-fit line, and take the gradient from a large triangle with its coordinates and unit shown. One clean example beats re-reading the theory.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026

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