New
New
Year 8

Negative rate of change from a graph

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

New
New
Year 8

Negative rate of change from a graph

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

Lesson details

Key learning points

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

Common misconception

Pupils may think lines with gradients 2 and -2 are parallel.

Lines have to have the exact same gradient to be parallel. A line with a negative gradient will intersect a line with a positive gradient .

Keywords

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

  • Absolute value - The absolute value of a number is its distance from zero.

  • Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

Use of ratio tables is key to overcoming most common mistakes. Pupils who are confident using ratio tables here, will find it easier to calculate gradient from coordinate pairs later on.
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.
Which of these is the correct explanation for how gradient is calculated?
rate of change in $$x$$ direction with respect to positive $$y$$ direction
rate of change in $$x$$ direction with respect to negative $$y$$ direction
rate of change in $$y$$ direction with respect to negative $$x$$ direction
Correct answer: rate of change in $$y$$ direction with respect to positive $$x$$ direction
Q2.
The gradients of all 4 lines are .
An image in a quiz
equal
even
negative
Correct answer: positive
straight
Q3.
What is the gradient of this line?
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Correct Answer: 4, four
Q4.
What is the gradient of this line?
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Correct Answer: 6, six
Q5.
Which of these tables of values show a relationship which will have a positive gradient when plotted?
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Correct answer: A
B
Correct answer: C
D
Correct answer: E
Q6.
Which is the correct ratio table for this graph?
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Correct Answer: An image in a quiz
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6 Questions

Q1.
Which of these graphs have a negative gradient?
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Correct answer: A (purple)
Correct answer: B (blue)
C (pink)
Correct answer: D (green)
Q2.
Match the graphs to the correct gradient.
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Correct Answer:A (purple),3

3

Correct Answer:B (black),2

2

Correct Answer:C (pink),1

1

Correct Answer:D (blue),-1

-1

Correct Answer:E (green),-2

-2

Q3.
What is the gradient of this line?
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Correct Answer: -3, negative 3, negative three
Q4.
What is the gradient of this line?
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$$-{3\over 2}$$
Correct answer: $$-{2\over 3}$$
$$-{1\over 2}$$
$$2\over 3$$
$$3\over 2$$
Q5.
Starting with the steepest, put these gradients in order of steepness.
1 - $$-8$$
2 - $$6$$
3 - $$5\over 2$$
4 - $$-1$$
5 - $$-{2\over 3}$$
6 - $$1\over 2$$
Q6.
Which lines would be parallel to the one shown if drawn on the same axes?
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Correct Answer: An image in a quiz
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Correct Answer: An image in a quiz
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