Thursday, 22 September 2016

Understanding: Inverse Proportion

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

Through the scenario...

It takes 1 person 100 days to paint a house.

With 2 persons, we will need 100÷2 days.
With 3 persons, we will need 100÷3 days.

Let the number of persons be x and the number of days be y

By tabulating the above scenario, we will get:

Now, to plot the points, we'll get:
[Notice that while the values decrease, the points do not fall on a straight line?]
[In other words, the decrease does not follow equal 'steps' like what we see in the linear graph]

By joining the dots, we get a reciprocal graph with the equation:

A standard reciprocal graph will look like this (appears in both 1st and 3rd quadrant):

Depending on the context - the part of the graph in the 3rd quadrant may not the relevant (e.g. in this case, the number of days and number of people could not be negative).

If we study the relationship carefully, this is an inverse relationship:

Since 100 is a constant value, we represent 100 by k . Hence, the above can be rewritten as:

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