Thursday, 22 September 2016

Understanding: Direct Proportion

[This is a recap of what was carried out in class on 21 Sep]

Through the scenario....

The ice cream vendor sells cones of ice cream at the price of $1.50 per cone. 

The total amount collected = price of 1 cone X number of cones sold
The total amount collected = $1.50 X number of cones sold
Hence, $1.50 is the rate. 

Instead of writing out in words, we let
  • Total amount collected be represented by y
  • Total number of cones sold represented by x
With this, we form the relationship
  • y = 1.5 x (where 1.5 is the rate)
In other words, 
  • when the number of cones sold increases, the amount collected will increase.
  • when the number of cones sold decreases, the amount collected will decrease.
y and x are variables because as one of them changes, the other changes.

1.5 remains constant as it is a fixed value that the vendor priced each cone of ice cream at.

Instead of writing 1.5, we let k to represent this constant value.

Hence, we can generalise the above as: 
  • y = k x (where k is the constant)

Applying what we learnt in the topic, Functions and Linear Graphs,
y = k  will be a linear graph, where k is the gradient and the line passes through the origin! 
Hence, we can represent it as: 

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