Year 8 - Maths
Defining features of linear relationships
Graphical representations of linear equations
Study Hub
Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unti we develop understanding of linear relationships and explore the key features of a linear equation such as the gradient, intercept and determining an equation from coordinate pairs.
Lesson Summary
You will learn to appreciate that there are two key elements to any linear relationship: rate of change and intercept point.
Key Notes
- There is always a common difference in an arithmetic sequence.
- There is always a constant rate of change on a linear graph.
- There is always an initial value in an arithmetic sequence.
- There is always an intercept point with the y-axis on a linear graph.
- These two features uniquely describe any linear relationship.
Vocabulary To Learn
- Rate of change: The rate of change is how quickly one variable changes with respect to another. If constant, there is a linear relationship.
- Intercept: An intercept is the coordinate where a line or curve meets a given axis.
Common Mistakes To Avoid
- The arithmetic sequence 5n+2 starts at 7 so the linear equation y=5x+2 'starts' somewhere.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There is always a common difference in an arithmetic sequence. There is always a constant rate of change on a linear graph.
2. Use this key word in a maths sentence and explain it clearly. 'Rate of change'
The rate of change is how quickly one variable changes with respect to another. If constant, there is a linear relationship. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The arithmetic sequence 5n+2 starts at 7 so the linear equation y=5x+2 'starts' somewhere. Correction: y=5x+2 has no start and no end; it goes on infinitely. However, all linear equations have a y-intercept and this helps define them.
More Lessons In This Unit
- Checking and securing plotting a relationship Study Guide
- Checking and securing understanding of plotting coordinates Study Guide
- Checking and securing understanding of plotting coordinates generated from a rule Study Guide
- Checking and securing understanding of plotting coordinates with technology Study Guide
- Features of linear relationships Study Guide
- Finding the equation of the line ay + bx + c = 0 Study Guide
- Finding the equation of the line y = mx + c Study Guide
- Negative rate of change from a graph Study Guide
- Positive rate of change from a graph Study Guide
- Problem solving with graphing linear relationships Study Guide
- Rate of change from a coordinate pair Study Guide
- The equation of a straight line Study Guide
- The intercept point Study Guide
- Using dynamic software to explore linear relationships Study Guide
Browse all guides in the Year 8 Maths guide library.