The rate of change is how one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.

Checking and securing understanding of reading from context-based graphs

Maths

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

Real-life graphs

Here is a distance-time graph of a journey. When was the object moving the fastest?

Which sections of this graph are impossible?

Object is moving at a constant speed away from home.

Object is moving at a constant speed towards home.

On this 'distance from home' graph, which of these best describes what is happening at a)?

Object is moving at its fastest speed away from home.

Object is moving at its slowest speed away from home.

Object is moving at its fastest speed towards home.

Object is moving at its slowest speed towards home.

On this 'distance from home' graph, which of these best describes what is happening at b)?

Assuming it is filled at a constant rate, which of these could be a depth-time graph for this container?

Assuming they were filled at a constant rate, which container could this depth-time graph represent?

If the rate of change between two variables is constant, then the relationship between them is __________

Which of these shows a constant rate of change between $$x$$ and $$y$$?

Which of these lines have negative gradient?

Starting with the steepest, put these lines in order of steepness.

The solution to the equation $$2-\frac{3}{5}x = -1$$ is $$x = $${{}}. Use the graph to help you.

Using this distance-time graph, calculate the distance travelled after 4 hours.

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Checking and securing understanding of reading from context-based graphs

Lesson outcome