Year 8 - Maths
Features of linear relationships
Graphical representations of linear equations
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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 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 recognise that linear relationships have particular algebraic and graphical features as a result of the constant rate of change.
Key Notes
- A linear graph can be described by its features.
- All the coordinates on the line fit the relationship.
- The relationship between the coordinates can be described algebraically.
- These linear relationships have particular features.
- You can move between the algebraic statement and the graphical representation and back using coordinates.
Vocabulary To Learn
- Linear: The relationship between two variables is linear when they change together at a constant rate and form a straight line when plotted.
Common Mistakes To Avoid
- Only equations in the form $$y=mx+c$$ are linear. All equations are linear.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A linear graph can be described by its features. All the coordinates on the line fit the relationship.
2. Use this key word in a maths sentence and explain it clearly. 'Linear'
The relationship between two variables is linear when they change together at a constant rate and form a straight line when plotted. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Only equations in the form $$y=mx+c$$ are linear. All equations are linear. Correction: There are many forms that linear equations can take, however they always share a common feature. The variables have exponents of $$1$$.
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
- Defining 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
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