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Year 8

Using dynamic software to explore linear relationships

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

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New
New
Year 8

Using dynamic software to explore linear relationships

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

Download all resources
Share activities with pupils

Lesson details

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

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 '$$c$$'.

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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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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

Exit quiz

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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: $$y=0.45-0.3x$$
$$y=0.45-1.5x$$
$$y=0.5-0.3x$$
$$y=0.3-0.45x$$