Year 10 - Maths
Checking and securing understanding of finding the equation of the line from coordinates
Linear graphs
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 unit pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.
Lesson Summary
You will learn to find the equation of the line from two coordinate pairs as well as from the gradient and one coordinate pair.
Key Notes
- The gradient can be found from two points by considering the change in y over the change in x
- The y-intercept can be found using the gradient and one of the points.
- By substituting the gradient and one coordinate pair into the general equation, you can find the y-intercept.
- The y-intercept occurs when the x value is zero.
- It is useful to check using the second point while understanding the limitations of this check.
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.
Common Mistakes To Avoid
- Writing equations of the form y = mx + c and getting the gradient and y-intercept the wrong way round.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The gradient can be found from two points by considering the change in y over the change in x. The y-intercept can be found using the gradient and one of the points.
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: Writing equations of the form y = mx + c and getting the gradient and y-intercept the wrong way round. Correction: Graphing software can be used to show that adding a constant is a translation of the graph. Remind pupils that the y-intercept is when x is zero which is why it is the constant in the equation. They can substitute x = 0 to check.
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 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
- Parallel linear graphs Study Guide
- Perpendicular linear graphs Study Guide
- Problem solving with linear graphs Study Guide
- Ratios in line segments on coordinate axes Study Guide
Browse all guides in the Year 10 Maths guide library.