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Learning intentions:
In this section we will examine:
- Relationships with a constant rates of change and their graphs.
Constant rate of change
A relationship with a constant rate is one where the the rate of change of one quantity with respect to another does not change. Graphically, they are characterised by linear lines where the gradient represents the rate of change.
Figure 1 - (L) positive constant rate of change, (M) constant zero rate of change (R) constant negative rate of change
10B - VIDEO EXAMPLE 1:
The volume of water in a bath as it is being emptied is shown on the graph below. Determine the rate at which the volume is changing with respect to time.
10B - VIDEO EXAMPLE 2:
Two cars are travelling away from the same location. Car A takes 30 minutes to drive 40 kilometres, while Car B takes 30 minutes to drive 50 kilometres. Determine the rate of change of distance with respect to time for Car A and Car B and graph the distance travelled against time for both cars.
Success criteria:
You will be successful if you can:
- Recognise constant rates of change and situations where they apply.
- Graph constant rates of change as a linear graph.
- Understand the relationship between the gradient and the rate of change.
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