Year 10 - Maths
Perpendicular linear graphs
Linear graphs
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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 consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.
Lesson Summary
You will learn to prove the relationship between the gradients of perpendicular lines.
Key Notes
- Two lines are perpendicular if they meet at right angles.
- The product of the gradients of two perpendicular lines is -1
- This can be derived from Pythagoras' theorem.
- The product of the gradients of two lines is -1 iff the lines are perpendicular.
Vocabulary To Learn
- Perpendicular: Two lines are perpendicular if they meet at right angles.
- IFF: IFF (If and only if) is an implication that goes both ways.
Common Mistakes To Avoid
- Perpendicular lines have to be drawn as a horizontal and vertical pair.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Two lines are perpendicular if they meet at right angles. The product of the gradients of two perpendicular lines is -1.
2. Use this key word in a maths sentence and explain it clearly. 'Perpendicular'
Two lines are perpendicular if they meet at right angles. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Perpendicular lines have to be drawn as a horizontal and vertical pair. Correction: Some pupils may struggle to see that two lines are perpendicular when they are not drawn horizontally and vertically. Drawing this on paper and then rotating the paper will help them see that it is the angle between the lines that matters.
More Lessons In This Unit
- Advanced problem solving with linear graphs Study Guide
- Checking and securing understanding of drawing linear graphs Study Guide
- Checking and securing understanding of drawing vertical and horizontal graphs Study Guide
- Checking and securing understanding of finding the equation of the line from coordinates Study Guide
- Checking and securing understanding of finding the equation of the line from the graph Study Guide
- Checking and understanding graphs showing direct proportion Study Guide
- Graphs showing inverse proportion Study Guide
- Identifying perpendicular linear graphs Study Guide
- Parallel and perpendicular lines on coordinate axes Study Guide
- Parallel linear graphs Study Guide
- Problem solving with linear graphs Study Guide
- Ratios in line segments on coordinate axes Study Guide
Browse all guides in the Year 10 Maths guide library.