Variation and Proportion
Ages 16–18Difficulty adapts to you
Variation and Proportion
Direct proportion has y = kx, so y ÷ x is constant. Inverse proportion has y = k/x, so xy is constant. Find the constant from known values before predicting an unknown value.
Your goals
- ✓You can model direct, inverse, and combined relationships between quantities.
- ✓You can use Variation and Proportion, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Variation and Proportion:
- Model direct, inverse, and combined relationships between quantities.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1If y is directly proportional to x and y = 12 when x = 3, then k = 4 and y = 4x.
- 2If y is inversely proportional to x and y = 5 when x = 4, then xy = 20 and y = 20/x.
Check these
- • Do not skip the meaning of a term or give a result without explaining what it means.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own variation and proportion example, solve it, and explain how you checked it.
Professor Wise Owl
Wisdom & Understanding“A wise learner asks questions. Be curious!”