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

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.

Modelling with graphs

Maths

In this unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In the future unit, other types of graphs are introduced and their key features identified.

In the prior unit, pupils considered geometric sequences and how they might be represented graphically. In this unit, pupils study the graphical representation to link features of the graph to its equation.

Graphical representations

The {{}} is a measure of how steep a line is.

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?

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.

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?

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.

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.

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

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

Which of these lines has the steepest gradient? 

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

This parabola models the flight of a cricket ball being thrown. Estimate the maximum height of the cricket ball.

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?

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 {{}}.

This lesson will be removed by end of Summer Term 2025.

Modelling with graphs

Lesson outcome

This lesson will be removed by end of Summer Term 2025.