Year 11 - Maths
Checking and securing understanding of direct proportion graphs
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 identify direct proportion graphs from their features and can use the graph to create an equation to algebraically model this relationship.
Key Notes
- Direct proportion can be recognised graphically.
- A direct proportion graph is always a straight line through the origin.
- The gradient is the constant of proportionality.
- The equation of the line can be found and this is the algebraic model of the relationship.
Vocabulary To Learn
- Direct proportion: Two variables are in direct proportion if they have a constant multiplicative relationship
- Gradient: The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction
- Intercept: An intercept is the point where a line or curve meets a given axis
Common Mistakes To Avoid
- Assuming that any linear graph with a constant positive gradient shows a directly proportional relationship.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Direct proportion can be recognised graphically. A direct proportion graph is always a straight line through the origin.
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: Assuming that any linear graph with a constant positive gradient shows a directly proportional relationship. Correction: Using examples in a context really helps here. E.g. 'I change £0. How many dollars do I get?, I travel 0 miles. How many kilometres have I travelled?
More Lessons In This Unit
- Abstract direct proportion Study Guide
- Abstract inverse proportion Study Guide
- Checking and securing understanding of inverse proportion graphs Study Guide
- Finding the constant of proportionality for direct proportion 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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