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      Solving a linear inequality graphically

      Lesson details

      Learning outcome

      I can extend my thinking to a linear inequality with 2 variables and can show this can be solved graphically to find a solution set.

      Key learning points

      1. A linear inequality involving two variables can be graphed
      2. A solid line indicates the solutions on the line are valid
      3. A dashed line indicates a strict inequality
      4. By testing points not on the line, you can determine the region that satisfies the inequality
      5. This region is the solution set

      Keywords

      • Region (inequalities) - A region is an area that graphically represents the solutions to one or more inequalities. Every coordinate pair within the region satisfies the inequalities that define the region.

      Common misconception

      Thinking that x = 4 is a line parallel to the x axis and that y = 4 is parallel to the y axis.

      Consider the points along the line. Writing valid coordinate pairs lets pupils identify which coordinate stays the same and which one changes.

      Teacher tip

      Pupils may benefit from having the number line representation displayed alongside the graphs in LC1 to help them recognise which solutions will be valid and which will not.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      $$x>7$$ is an algebraic representation of...

      Correct answer: an inequality.
      an expression.
      an equation.

      Q2.
      Which of these values satisfy the inequality? $$x>7$$

      $$x=7$$
      $$x=6$$
      Correct answer: $$x=8$$
      Correct answer: $$x=7.5$$
      Correct answer: $$x= 165\;672$$

      Q3.
      Which is this line?

      An image in a quiz
      $$y=4x$$
      $$y=4$$
      Correct answer: $$x=4$$
      $$4$$

      Q4.
      Which is this line?

      An image in a quiz
      $$x=-2$$
      $$-2$$
      Correct answer: $$y=-2$$
      $$y=-2x$$
      $$y=x-2$$

      Q5.
      Which of these coordinate pairs sit on this linear graph?

      An image in a quiz
      Correct answer: $$(0,-5)$$
      $$(-5,0)$$
      Correct answer: $$(3,4)$$
      $$(1,2)$$
      Correct answer: $$(0.5,-3.5)$$

      Q6.
      What is the equation of this linear graph?

      An image in a quiz
      $$y=3x$$
      $$y=5+3x$$
      Correct answer: $$y=3x-5$$
      $$y=5x-3$$
      $$x=3y-5$$

      6 Questions

      Q1.
      A is an area that graphically represents the solution to an inequality. We can label this area with an 'R'.

      Correct Answer: region

      Q2.
      Which inequality represents this region?

      An image in a quiz
      $$x\le5$$
      $$x\geq5$$
      Correct answer: $$x<5$$
      $$y<5$$
      $$y>5$$

      Q3.
      Which inequality represents this region?

      An image in a quiz
      $$y<-4$$
      $$y\le-4$$
      $$y>-4$$
      Correct answer: $$y\geq-4$$
      $$x>-4$$

      Q4.
      Which inequality is satisfied by this region?

      An image in a quiz
      $$2<x<5$$
      $$2<x<4$$
      $$2\le{x}\le5$$
      $$2\le{x}<5$$
      Correct answer: $$2<{x}\le5$$

      Q5.
      Which inequality is represented graphically here?

      An image in a quiz
      $$x>{3-y}$$
      $$y<x-3$$
      $$y\le{x-3}$$
      Correct answer: $$y<{3-x}$$
      $$y\le{3-x}$$

      Q6.
      This is the region that does not satisfy the inequality...

      An image in a quiz
      $$y>4-2x$$
      $$y<4-2x$$
      $${y}\geq{4-2x}$$
      Correct answer: $${y}\le{4-2x}$$

      To help you plan your 11 maths lesson on: Solving a linear inequality graphically, download all teaching resources for free and adapt to suit your pupils' needs...