New
New
Year 8

Positive rate of change from a graph

I can calculate the positive rate of change (gradient) from a graph.

New
New
Year 8

Positive rate of change from a graph

I can calculate the positive rate of change (gradient) from a graph.

Lesson details

Key learning points

  1. Graphs can be described by looking at how quickly they rise.
  2. The amount y changes when x increases by one is the rate of change and is called the gradient.
  3. The gradient will be positive if y increases as the graph moves to the right.
  4. The gradient can be found from any linear graph.
  5. The gradient tells you important information about the relationship.

Common misconception

Pupils count squares to calculate gradient instead of looking at scales.

Encourage pupils to pick points on the graph to use to find the gradient and write down the coordinates rather than count squares.

Keywords

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

Challenge pupils to draw their own lines with different gradients, mini whiteboards with squares or printed axis in plastic wallets can be helpful for this. Make it clear that the axis have a step of 1 for this.
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).

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6 Questions

Q1.
The coordinate (0,0) can also be called the .
Correct Answer: origin, Origin
Q2.
What is the step on the $$x$$ axis of this graph?
An image in a quiz
Correct answer: 0.5
1
2
10
Q3.
What is the missing number in this table of values for the equation $$y=5x-3$$ ?
An image in a quiz
Correct Answer: 7
Q4.
A drink is made from 3 litres of juice and 9 litres of soda. Use the ratio table to work out the amount of soda needed for 1 litre of juice.
An image in a quiz
Correct Answer: 3, 3 litres, 3 l, 3L
Q5.
What is the missing value in this ratio table?
An image in a quiz
$$3\over 5$$
1.6
Correct answer: $$5\over 3$$
3
15
Q6.
A table of values is shown for the relationship $$y = 11 - 3x$$. Which of these is true for this relationship?
An image in a quiz
Correct answer: For every change of +1 in $$x$$ there is a change of -3 in $$y$$
For every change of +1 in $$x$$ there is a change of +3 in $$y$$
For every change of +1 in $$y$$ there is a change of -3 in $$x$$
For every change of +2 in $$x$$ there is a change of -5 in $$y$$
Correct answer: For every change of +3 in $$x$$ there is a change of -9 in $$y$$

6 Questions

Q1.
Which of these best describes the gradient?
Correct answer: How much the $$y$$ values change for every 1 increase in $$x$$
How much the $$x$$ values change for every 1 increase in $$y$$
How much the $$y$$ values change for every 1 decrease in $$x$$
How much the $$x$$ values change for every 1 decrease in $$y$$
Q2.
Which of these lines have a positive gradient?
An image in a quiz
Correct answer: A
B
Correct answer: C
D
Q3.
The gradient of this line is .
An image in a quiz
Correct Answer: 2, two
Q4.
Match the lines labelled A, B, C, D with the correct gradient.
An image in a quiz
Correct Answer:A (green),1

1

Correct Answer:B (pink),$$1\over 2$$

$$1\over 2$$

Correct Answer:C (blue),4

4

Correct Answer:D (purple),3

3

Q5.
What is the gradient of this line?
An image in a quiz
$$2\over 5$$
2
Correct answer: $$5\over 2$$
3
5
Q6.
What is the gradient of this line?
An image in a quiz
Correct Answer: 5