New
New
Year 9

Modelling with graphs

I can model real-life situations graphically.

New
New
Year 9

Modelling with graphs

I can model real-life situations graphically.

Lesson details

Key learning points

  1. Distance-time graphs tell you how far you have travelled over a period of time.
  2. By reading the graph, you can tell if there is mistake with it.
  3. You can sketch a graph based on the information you have been given.
  4. Important given values should be marked on your sketch.

Common misconception

The line on a distance time graph can go in any direction.

The line may be horizontal, time changing without a change in distance, but it can not be vertical. That would be a change in distance without a change in time. Additionally, our line cannot go backwards; time is always moving forwards.

Keywords

  • Rate of change - The rate of change is how quickly one variable changes in relation to another.

  • Gradient - The gradient is a measure of how steep a line is, calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

Use a real-life example from your classroom. Ask a pupil to describe a journey they take, and ask the rest of the class to sketch the distance time graph.
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).

Loading...

6 Questions

Q1.
The of change is how quickly one variable changes in relation to another.
Correct Answer: rate
Q2.
Which of these lines has the steepest gradient?
An image in a quiz
Correct answer: Line a
Line b
Line c
Q3.
Look at this graph. What is the value of $$x$$ when $$y=5$$?
An image in a quiz
$$x=1$$
$$x=2$$
Correct answer: $$x=3$$
$$x=4$$
Q4.
This parabola models the flight of a cricket ball being thrown. Estimate the maximum height of the cricket ball.
An image in a quiz
9.8 metres
10 metres
Correct answer: 10.2 metres
11 metres
21 metres
Q5.
Laura is plotting the graph of the line $$3y + 4x=12$$. She only wants to plot two points. Which of these points would be the best points for Laura to use?
Correct answer: When $$x=0$$
When $$x=1$$
When $$x=2$$
Correct answer: When $$x=3$$
When $$x=4$$
Q6.
Jun wants to draw the graph of $$y = 0.4x + 3.2$$ for positive values of $$x$$. The coordinates of the first point on the line that has positive integer coordinates are .
Correct Answer: (2, 4), (2,4)

6 Questions

Q1.
The is a measure of how steep a line is.
Correct Answer: gradient
Q2.
The distance-time graph shows Sofia's journey to a friend's house. $$d$$ is the distance in metres and $$t$$ is the time in minutes. Which part of the journey is Sofia moving at the greatest speed?
An image in a quiz
Part a
Part b
Part c
Q3.
The distance-time graph shows Andeep's journey to the shops. $$d$$ is the distance in metres from Andeep's house and $$t$$ is the time in minutes. Altogether Andeep's journey takes minutes.
An image in a quiz
Correct Answer: 70
Q4.
The distance-time graph shows Andeep's journey to the shops. $$d$$ is the distance in metres and $$t$$ is the time in minutes. Which segments show Andeep has stopped?
An image in a quiz
A
Correct answer: B
C
Correct answer: D
E
Q5.
The distance-time graph shows Andeep's journey to the shops. $$d$$ is the distance in metres from Andeep's house and $$t$$ is the time in minutes. Altogether Andeep has walked kilometres.
An image in a quiz
Correct Answer: 2, two
Q6.
Izzy has drawn this distance-time graph. Which of these statements explain what is wrong with Izzy's graph.
An image in a quiz
A There should not be any sections with a positive gradient.
B There should not be any sections with a negative gradien
Correct answer: C There should not be any vertical sections.
D There should not be any horizontal sections.
Correct answer: E There should not be any sections where time goes backward.