Two quantities are directly proportional if doubling one doubles the other. Their graph is a straight line through the origin, and the ratio y ÷ x is the same for every pair of results. This constant is the gradient, and it often has a physical meaning, like the spring constant or resistance.
A straight line that does not pass through the origin shows a linear relationship but not direct proportion. In an inverse relationship, as one quantity doubles, the other halves, and the graph is a curve. Checking ratios in a results table is a quick test for proportion.
Worked example
Masses 100, 200, 300 g give extensions 30, 60, 90 mm. Are they proportional?
- Ratios: 30 ÷ 100 = 0.3, 60 ÷ 200 = 0.3, 90 ÷ 300 = 0.3.
- The ratio is constant.
Answer:Yes: extension is directly proportional to mass (0.3 mm per g).
Key words
- directly proportional
- y ÷ x is constant; line through the origin
- linear
- a straight-line graph
- inversely proportional
- one doubles as the other halves
- constant
- a value that stays the same
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