Year 11 - Maths
Finding the constant of proportionality for direct proportion
Direct and inverse proportion
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils learn how to represent direct and inverse proportion algebraically as an extension of work done in the linear graphs unit.
Lesson Summary
You will learn to use the general form for a directly proportional relationship to find k.
Key Notes
- Direct proportion equations are of the form y = kx
- k is the constant of proportionality and it is also the gradient of the graph.
- To find the gradient, k, you can use two sets of coordinates (pairs of values).
Vocabulary To Learn
- Direct proportion: Two variables are in direct proportion if they have a constant multiplicative relationship
Common Mistakes To Avoid
- Failing to recognise that x/2 is the same as 1/2 × x and therefore shows a directly proportional relationship where the value of k is 1/2.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Direct proportion equations are of the form y = kx. k is the constant of proportionality and it is also the gradient of the graph.
2. Use this key word in a maths sentence and explain it clearly. 'Direct proportion'
Two variables are in direct proportion if they have a constant multiplicative relationship. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Failing to recognise that x/2 is the same as 1/2 × x and therefore shows a directly proportional relationship where the value of k is 1/2. Correction: It is useful to go back to looking at unit fractions. E.g. 2/3 = 1/3 × 2 and 7/9 = 1/9 × 7, etc. And, then look at algebraic terms leading up to for example, 2x/3. 'What is the the multiplier?'.
More Lessons In This Unit
- Abstract direct proportion Study Guide
- Abstract inverse proportion Study Guide
- Checking and securing understanding of direct proportion graphs Study Guide
- Checking and securing understanding of inverse proportion graphs Study Guide
- Finding the constant of proportionality for directly proportional relationships Study Guide
- Finding the constant of proportionality for inverse proportion Study Guide
- Problem solving with direct and inverse proportion Study Guide
- Proportion modelled algebraically Study Guide
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