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Year 9 - Maths

Graphically solving two linear graphs that intersect

Graphical representations

Unit Summary

In this unit pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.

Lesson Summary

You will learn to recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations.

Key Notes

  • More than one linear graph can be drawn on the same set of axes.
  • A pair of coordinates which lay on the line satisfy the equation of the line.
  • The pair of coordinates for the point of intersection satisfy both equations.
  • Graphical software can be used to show this visually.

Vocabulary To Learn

  • Linear: The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Common Mistakes To Avoid

  • There is only one way to solve linear equations; by manipulation and isolating the variable(s).

3 Quick Questions (With Answers)

1. Solve this in steps: explain the method from this lesson and why each step matters.

More than one linear graph can be drawn on the same set of axes. A pair of coordinates which lay on the line satisfy the equation of the line.

2. Use this key word in a maths sentence and explain it clearly. 'Linear'

The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: There is only one way to solve linear equations; by manipulation and isolating the variable(s). Correction: When we plot more than one linear equation on a graph we can use the intersection to find the solution.

More Lessons In This Unit

Browse all guides in the Year 9 Maths guide library.