Year 8 - Maths
The equation of a straight line
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 appreciate that writing linear equations in the form y = mx + c helps to reveal the structure.
Key Notes
- Linear relationships can be written in a variety of algebraic forms.
- It is possible to identify the gradient and y-intercept when the equation is written in the form y=mx+c.
- The m comes from the French "monter" (to climb/ascend) and the c from "commencer" (to start).
- Linear equations can be rearranged in order to reveal the gradient and y-intercept.
Vocabulary To Learn
- Equation of a line: Any equation whose graph forms a straight line.
- Coefficient: A constant numerical multiplier of the variables in a term.
- Constant: A term that does not change; it contains no variables.
Common Mistakes To Avoid
- Pupils may think graphs are only linear if written in the form y=mx+c
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Linear relationships can be written in a variety of algebraic forms. It is possible to identify the gradient and y-intercept when the equation is written in the form y=mx+c.
2. Use this key word in a maths sentence and explain it clearly. 'Equation of a line'
Any equation whose graph forms a straight line. 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 graphs are only linear if written in the form y=mx+c. Correction: Use the first learning cycle as an opportunity to show graphs in many formats. y=mx+c makes the gradient and y intercept clear.
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
- 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 intercept point Study Guide
- Using dynamic software to explore linear relationships Study Guide
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