3Thavo §7.2 Directly and inversely proportional

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§ 7.2 Directly and inversely proportional

Before working on this paragraph, let's look at these words and their meaning first!

Directly proportional 1.

 Proportional is 'evenredig' in Dutch. 

Question: But what does 'evenredig' mean?

All think about this!

Directly proportional 2.

Answer: Proportional or 'evenredig' means in Maths that 

a variable gets bigger when another variable gets bigger.

Directly proportional 3.

Now we added the word 'directly' and it becomes very concrete:

When x becomes 3 times as large, then y also becomes 3 times as large.

In a formula:      y = 6x  or  y = 10x

For example: fill in x = 2 in y = 6x    We get y = 6 x 2 = 12

Now fill in x = 6 (so 3 times as large as 2):     y = 6 x 6 = 36

If we now compare 12 to 36, we see that y is done x 3 too!           

For example:

 y = 5x  Now divide by 5, you get

y/x = 5  !

Homework time!

Using what you just learnt, try to do the exercises 8 and further.

Skip the Introduction.

Later on this LessonUp will be continued.

Inversely proportional

From exercise 13 on you need some more information.

This we will go through together, right now!

It is about another kinda proportionality.

Question: What does 'Inversely' mean?

Inversely?!

Inversely means: 'omgekeerd',

 in good German.

Let's see what this means for our Math subject.

Task: Find at least 2 differences

between the tables for 'Directly proportional' and 'Inversely proportional'.

Look up both tables, on pages 250 and 252!

Solution to task:

Differences:

1. For Directly prop., if you do x times 4, you also do y times 4,

for Inversely prop., if you do x times 4, you do y divided by 4!

2. For Inversely prop. the product (that is doing: times)

stays the same always, for Directly proportional this is not the case.

Finally...

For Directly proportional you were shown a graph.

Watch Theory p.250 again: a straight line, through the origin.

But...why is there no graph shown for Inversely proportional?!

Anyway, look at page 255!

This kinda graph is called a HYPERBOLA.

Homework time again!

Good luck and make sure you do not have that much homework.

What did you learn this lesson?