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      Problem solving with linear graphs

      I can use my knowledge of linear graphs to solve problems.

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      Lesson 8 of 8
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      • Year 10

      Problem solving with linear graphs

      I can use my knowledge of linear graphs to solve problems.

      Lesson details

      Key learning points

      1. The shape of a graph can be used to identify its equation.
      2. Either the graphs or the equations can be used to identify parallel lines.

      Keywords

      • Midpoint - The midpoint of a line segment is halfway between the two end points.

      Common misconception

      Pupils may not appreciate all the steps required to prove what type of shape is shown.

      A warm-up for the lesson could be to review properties of shapes. Consider describing a shape, one property at a time. How much information is needed before pupils can be certain they know which shape is being described?

      Pupils may benefit from recreating the shapes themselves. This could be done on Desmos, drawing on paper or with Geoboards.
      Teacher tip

      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

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      6 Questions

      Q1.
      What number is halfway between 7 and 19?

      Correct Answer: 13

      Q2.
      Which of these coordinates are on the line $$x = 2$$?

      Correct answer: (2, -2)
      (0, 2)
      (-2, 2)
      Correct answer: (2, 2)
      Correct answer: (2, 7.1)

      Q3.
      Which of these lines passes through the coordinates (2, 8) and (5, 8)?

      $$x = 2$$
      $$x = 8$$
      $$y = 5$$
      Correct answer: $$y = 8$$
      $$x + y = 10$$

      Q4.
      lines are straight lines which are always the same non-zero distance apart.

      Correct Answer: Parallel, parallel

      Q5.
      The gradient of this line is .

      An image in a quiz
      Correct Answer: 3, three

      Q6.
      The gradient of the line passing through (5, 5) and (9, -3) is .

      Correct Answer: -2, negative 2, negative two, - 2

      Assessment exit quiz

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      6 Questions

      Q1.
      What is the coordinate of the midpoint of the line segment AB?

      An image in a quiz
      (4, 6)
      Correct answer: (5, 4)
      (5, 5)
      (6, 4)
      (10, 8)

      Q2.
      What is the coordinate of the midpoint of the line segment AB?

      An image in a quiz
      (-3, 2)
      Correct answer: (1, 5)
      (2, 4)
      (2, 6)
      (3, 5)

      Q3.
      Point P has coordinates (3, -8) and point Q has coordinates (10, -2). What is the coordinate of the midpoint of PQ?

      (5, -5)
      (5, -4)
      (6, -6.5)
      Correct answer: (6.5, -5)
      (7, -5)

      Q4.
      Point A has coordinates (6, 2) and B has coordinates (12, 0). Line L has equation $$y = 2x - 5.$$ What is the equation of the line parallel to L which passes through the midpoint of AB?

      An image in a quiz
      $$y = -5x-15$$
      $$y = 9-5x$$
      $$y = 8-2x$$
      $$y = 2x-14$$
      Correct answer: $$y = 2x-17$$

      Q5.
      If shape ABCD is a parallelogram, which of these statements would have to be true?

      An image in a quiz
      The line segments AB and BC have the same gradient.
      Correct answer: The line segments AB and DC have the same gradient.
      Correct answer: The line segments AD and BC have the same gradient.
      The line segment AB has a smaller gradient than the line segment BC.

      Q6.
      Jacob plots four points A, B, C on a graph. Jacob says he can join the points to form a parallelogram. Why is Jacob incorrect?

      An image in a quiz
      AB is not parallel to BC.
      AD is not parallel to BC.
      Correct answer: AB is not parallel to DC.
      The side lengths are not all the same length.
      The midpoint of AC is different to the midpoint of BD.

      Lesson appears in

      UnitMaths / Linear graphs

      Maths

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