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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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Lesson 14 of 15

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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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Lesson details

Key learning points

Dynamic software can be used to investigate how the gradients affects the line.
Dynamic software can be used to investigate how the intercept affects the line.
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 '$$c$$'.

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 (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge 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?

$$-2$$

$$-1$$

$$1$$

$$2$$

Correct answer: $$3$$

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

Correct answer: B

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

$$(-4,2)$$

$$(-3,0)$$

$$(-2,-2)$$

$$(-1,-4)$$

Correct answer: $$(0,-6)$$

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

Correct Answer: +4, 4, four

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

Correct Answer: +2, 2, two

Assessment 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?

$$y=2x$$

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.

Correct answer: $$y=0.45-0.3x$$

$$y=0.45-1.5x$$

$$y=0.5-0.3x$$

$$y=0.3-0.45x$$

Lesson appears in

UnitMaths / Graphical representations of linear equations

Maths

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Using dynamic software to explore linear relationships

Using dynamic software to explore linear relationships

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Relationships in the form of $$y=mx+c$$ will give us a .

Q2.What is the gradient of this line?

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

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

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

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

Assessment exit quiz

6 Questions

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

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

Q3.What is the equation of this line?

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

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

Q6.Calculate the equation of the line.

Lesson appears in

UnitMaths / Graphical representations of linear equations

Maths

Q1.
Relationships in the form of $$y=mx+c$$ will give us a .

Q2.
What is the gradient of this line?

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

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

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

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

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

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

Q3.
What is the equation of this line?

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

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

Q6.
Calculate the equation of the line.