Modelling with graphs | Maths | Quizalize & Oak National Academy

Starter quiz

The ______ of change is how quickly one variable changes in relation to another.

'rate' ✓
Which of these lines has the steepest gradient?

Line a ✓

Line b

Line c
Look at this graph. What is the value of $x$ when $y=5$ ?

$x=1$

$x=2$

$x=3$ ✓

$x=4$
This parabola models the flight of a cricket ball being thrown. Estimate the maximum height of the cricket ball.

9.8 metres

10 metres

10.2 metres ✓

11 metres

21 metres
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?

When $x=0$ ✓

When $x=1$

When $x=2$

When $x=3$ ✓

When $x=4$
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 ______.

'(2, 4)' ✓

Exit quiz

The ______ is a measure of how steep a line is.

'gradient' ✓
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?

Part a

Part b

Part c ✓
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.

'70' ✓
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?

A

B ✓

C

D ✓

E
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.

'2' ✓
Izzy has drawn this distance-time graph. Which of these statements explain what is wrong with Izzy's graph.

A There should not be any sections with a positive gradient.

B There should not be any sections with a negative gradien

C There should not be any vertical sections. ✓

D There should not be any horizontal sections.

E There should not be any sections where time goes backward. ✓

Worksheet

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Video

Lesson Details

Key learning points

Distance-time graphs tell you how far you have travelled over a period of time.
By reading the graph, you can tell if there is mistake with it.
You can sketch a graph based on the information you have been given.
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.