# 2TH §1.1 Linear relations

§1.1 Linear relations
Let's first see what you will learn today!
See next slide.
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Slide 1: Slide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 26 slides, with interactive quizzes and text slides.

Lesson duration is: 45 min

## Items in this lesson

§1.1 Linear relations
Let's first see what you will learn today!
See next slide.

#### Slide 1 -Slide

The goals for this paragraph are:

Let's first do an exercise together!

#### Slide 2 -Slide

Schermafbeelding 2021-07-27 om 10.13.58
Key in your answer in the next slide.

Key in your answer in the next slide.

#### Slide 3 -Slide

a. How many euros did Olav borrow?
timer
0:15
A
-15
B
15
C
165
D
-165

#### Slide 4 -Quiz

Schermafbeelding 2021-07-27 om 10.13.58
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.

#### Slide 5 -Slide

Schermafbeelding 2021-07-27 om 10.14.10
Ana

Answer question b in the next slide.

timer
0:20
A
-15
B
15
C
165

#### Slide 7 -Quiz

Schermafbeelding 2021-07-27 om 10.14.10
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).

#### Slide 8 -Slide

Schermafbeelding 2021-07-27 om 10.14.17
Again:

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

#### Slide 9 -Slide

c. How many months?
Calculate this!
timer
0:45
A
10
B
11
C
12

#### Slide 10 -Quiz

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.

#### Slide 12 -Slide

Question:
There are 2 formulas:
d = 165 - 15n   and
s = 15 - 3a
Describe why the shape of both formulas is the same.
ANS

#### Slide 13 -Slide

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

#### Slide 14 -Mind map

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

#### Slide 15 -Slide

Schermafbeelding 2021-07-27 om 10.14.32

#### Slide 16 -Slide

When is a formula a linear formula?
(= one of the two goals for today!)
A
when it describes a bended (gebogen) line
B
when it describes a vertical line
C
when it describes a straight line
D
when the graph goes through the origin, (0,0)

#### Slide 17 -Quiz

Solution
A linear formula describes a GRAPH in the form of
a STRAIGHT LINE.

#### Slide 19 -Slide

Now we look at some tables.
Not a table that you now have in front of you,
but a paper table, filled with numbers!

#### Slide 20 -Slide

Schermafbeelding 2021-07-27 om 10.18.52
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 !

timer
0:25
A
yes, -3
B
yes, 1
C
yes, 3
D
no

#### Slide 22 -Quiz

Schermafbee om 10.18.52
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'.

#### Slide 23 -Slide

om 10.20.23
Schermafbeelding 2021-07-27 om 11.08.32

om 10.20.23

#### Slide 25 -Slide

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