2TH §1.1 Linear relations

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• Middelbare school
• havo, vwo
• Leerjaar 2

§1.1 Linear relations

Let's first see what you will learn today!

See next slide.

The goals for this paragraph are:

Let's first do an exercise together!

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Key in your answer in the next slide.

Key in your answer in the next slide.

a. How many euros did Olav borrow?

1. -15
2. 15
3. 165
4. -165

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Key in your answer in the next slide.S

Solution:

In the formula you see that at the start there is a 165 euros debt.

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Ana

Answer question b in the next slide.

1. -15
2. 15
3. 165

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Ana

Solution:

The part - 15n means that he pays back 15 euros per month.

The minus sign indicates that for every month (n) 15 euros are subtracted from the total debt (schuld).

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Again: 

Again: Answer in the Next Slide (let's call this ANS).

c. How many months?
Calculate this!

1. 10
2. 11
3. 12

1c      Solution:

The formula is  d = 165 - 15n

Every month 15 euros is paid back.

So we do:        165 : 15 = 11

11 months it takes Olav to pay it all back!

Now it is time for a joke.

Question:

There are 2 formulas:

d = 165 - 15n   and

s = 15 - 3a

Describe why the shape of both formulas is the same.

ANS

The shape is the same, because.....

Solution:

d = 165 - 15n   and s = 15 - 3a

There are more good answers:

- because all the time a certain amount is made smaller in the course of time.

- there are 2 variables (letters) in both formulas

- etcetera

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When is a formula a linear formula?
(= one of the two goals for today!)

1. when it describes a bended (gebogen) line
2. when it describes a vertical line
3. when it describes a straight line
4. when the graph goes through the origin, (0,0)

Solution

A linear formula describes a GRAPH in the form of

 a STRAIGHT LINE.

Now we look at some tables.

Not a table that you now have in front of you, 

but a paper table, filled with numbers!

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ioi

As you can see, the increase (toename) in the top row is always the same. This increase is  + 1.

But is the increase in the bottom row also the same?

If so, what is this increase?

ANS !

1. yes, -3
2. yes, 1
3. yes, 3
4. no

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iSol

Solution: 

The increase in the bottom row is 3,

because from -3 to 0 it is 3 up,

from 0 to 3 it is 3 up again. Etcetera.

REMARK: the numbers in the top row are CONSECUTIVE, that is:

'opeenvolgend'.

 om 10.20.23

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 om 10.20.23

Homework time

Do exercise 3-7 (page 11-12)

Was it difficult? Do the Support path S2 and S7

Was it easy? Do the Challenge Exercise C1