Year 8 - Maths
Negative rate of change from a graph
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 calculate the negative rate of change (gradient) from a graph.
Key Notes
- Graphs can be described by looking at how quickly they fall.
- The amount y decreases when x increases by one is the rate of change and is called the gradient.
- The gradient will be negative if y decreases as the graph moves to the right.
- The gradient can be found from any linear graph.
- The gradient tells us important information about the relationship.
Vocabulary To Learn
- Gradient: The gradient is a measure of how steep a line is.
- Absolute value: The absolute value of a number is its distance from zero.
- Parallel: Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.
Common Mistakes To Avoid
- Pupils may think lines with gradients 2 and -2 are parallel.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Graphs can be described by looking at how quickly they fall. The amount y decreases when x increases by one is the rate of change and is called the gradient.
2. Use this key word in a maths sentence and explain it clearly. 'Gradient'
The gradient is a measure of how steep a line is. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may think lines with gradients 2 and -2 are parallel. Correction: Lines have to have the exact same gradient to be parallel. A line with a negative gradient will intersect a line with a positive gradient .
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
- 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
- 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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