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      Using dynamic software to explore linear relationships

      Lesson details

      Learning outcome

      I can solve a range of problems involving graphical and algebraic aspects of linear relationships using dynamic software.

      Key learning points

      1. Dynamic software can be used to investigate how the gradients affects the line.
      2. Dynamic software can be used to investigate how the intercept affects the line.
      3. Dynamic software can be used to investigate connections between lines, coordinates, tables and algebraic representations

      Keywords

      • Gradient - The gradient is a measure of how steep a line is.

      • Intercept - An intercept is the coordinate where a line or curve meets a given axis.

      Common misconception

      From the line $$y=x$$ to $$y=x+1$$ to $$y=x-1$$ the lines are moving left/right rather than up/down.

      It can be shown by using a $$(x,c)$$ coordinate in desmos. That coordinate moves up and down with the change in '$$c$$'.

      Teacher tip

      Get the pupils to all make a 'slider' for '$$c$$' in $$y=x+c$$ and hit play. Get pupils to pick a specific point and look at how that point on the line moves as 'c' changes.

      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.
      Relationships in the form of $$y=mx+c$$ will give us a .

      curve when graphed
      Correct answer: straight line graph
      increasing sequence
      increasing graph

      Q2.
      What is the gradient of this line?

      An image in a quiz
      $$-2$$
      $$-1$$
      $$1$$
      $$2$$
      Correct answer: $$3$$

      Q3.
      Which of these coordinates is $$(0,3)$$?

      An image in a quiz
      A
      Correct answer: B
      C
      D

      Q4.
      Which of these coordinates sits on the $$y$$-axis?

      An image in a quiz
      $$(-4,2)$$
      $$(-3,0)$$
      $$(-2,-2)$$
      $$(-1,-4)$$
      Correct answer: $$(0,-6)$$

      Q5.
      This table of values will plot a linear relationship with what gradient?

      An image in a quiz
      Correct Answer: +4, 4, four

      Q6.
      This table of values will plot a linear relationship with what gradient?

      An image in a quiz
      Correct Answer: +2, 2, two

      6 Questions

      Q1.
      For relationships in the form $$y=mx+c$$ the value of $$m$$ determines the .

      coordinates
      $$y$$-intercept
      $$x$$-intercept
      scale of the axes
      Correct answer: gradient

      Q2.
      What of these statements will be true about the lines $$y=3x$$, $$y=7x$$, and $$y=-2x$$?

      Correct answer: They will all have a different gradient.
      They will be parallel lines.
      Correct answer: One and only one of the lines will have a negative gradient.
      They will all have a different $$y$$-intercept.

      Q3.
      What is the equation of this line?

      An image in a quiz
      $$y=2x$$
      Correct answer: $$y={1\over2}x$$
      $$y=x+2$$
      $$y=x+{1\over2}$$

      Q4.
      Which statements are true about the lines $$y=x+5$$, $$y=x+9$$, and $$y=x+0.5$$?

      Correct answer: They have the same gradient.
      Correct answer: They are parallel lines.
      The have the same $$y$$-intercept.
      They have common coordinates.

      Q5.
      The lines $$y=4-7x$$ and $$y=-0.1-7x$$ have the same .

      Correct Answer: gradient, Gradient

      Q6.
      Calculate the equation of the line.

      An image in a quiz
      Correct answer: $$y=0.45-0.3x$$
      $$y=0.45-1.5x$$
      $$y=0.5-0.3x$$
      $$y=0.3-0.45x$$

      To help you plan your 8 maths lesson on: Using dynamic software to explore linear relationships, download all teaching resources for free and adapt to suit your pupils' needs...