Year 10 - Maths
Parallel 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 identify, from their equations or graphs, whether two lines are parallel.
Key Notes
- Two lines are parallel if they are equidistant and never touch.
- For linear graphs, the rate of change is constant.
- If the gradients are the same then the linear graphs may be parallel.
- The y-intercepts must be different, otherwise the lines are the same.
Vocabulary To Learn
- 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 coordinate where a line or curve meets a given axis.
- Parallel: Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.
Common Mistakes To Avoid
- Lines are parallel if they have the same gradient.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Two lines are parallel if they are equidistant and never touch. For linear graphs, the rate of change is constant.
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. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Lines are parallel if they have the same gradient. Correction: Lines are parallel if they have the same gradient and different y-intercepts. Two lines are parallel if they are straight lines that are always the same non-zero distance apart.
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
- Perpendicular linear graphs Study Guide
- Problem solving with linear graphs Study Guide
- Ratios in line segments on coordinate axes Study Guide
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