# 1TH/vwo §6.2 Graphs from formulas

1TH/vwo §6.2 Graphs from formulas
(you may skip 9, 10 and 11 as we will do a lot together)
Some TABLES to be made and many
GRAPHS to be drawn in this paragraph.
First we do a part of the paragraph together.
Work hard on the coming tasks,  skipping some exercises later.
1 / 35
Slide 1: Tekstslide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 1

In deze les zitten 35 slides, met interactieve quizzen en tekstslides.

Lesduur is: 50 min

## Onderdelen in deze les

1TH/vwo §6.2 Graphs from formulas
(you may skip 9, 10 and 11 as we will do a lot together)
Some TABLES to be made and many
GRAPHS to be drawn in this paragraph.
First we do a part of the paragraph together.
Work hard on the coming tasks,  skipping some exercises later.

#### Slide 1 -Tekstslide

Materials ....
+ Take before you the right things:
+ pencil, pen, geo triangle or ruler, eraser
+ GRAPHS are always drawn with a PEN + GEO/RULER !
+ Notebook and Textbook 1A, p.208

#### Slide 2 -Tekstslide

7
This is the Theory.
But HOW do you do these steps?!
Next slide shows us an example.

5

ANS!

#### Slide 4 -Tekstslide

Steps of 60 is fine, because ...
A
you have to put 300 on the vertical axis; then you need 300 : 60 = 5 cm.
B
the time goes from 0 to 5
C
the distances go up by 60 all the time
D
there is no zigzag needed

#### Slide 5 -Quizvraag

6
Points of attention:
+ when drawing a GRAPH, don't forget making a TABLE!
+ Scale:  on the vertical axis 60 (km?) is put in 1 cm, so that you cover 300 km.
+ The graph is a straight line because all points lie on one line.
+ Labelling of the axes has not been forgotten.
+ Note that there is no reason for a zigzag.

#### Slide 6 -Tekstslide

What to do first, before plotting the graph?

First you ....

Solution:
First you ...
MAKE A TABLE !
As follows:

#### Slide 9 -Tekstslide

the FILL IN the Table above!

timer
2:00

#### Slide 10 -Tekstslide

COMPARE your TABLE with the one below:

#### Slide 11 -Tekstslide

Before you go on with this task, there come a few questions about it.

Note: only the EVEN number are used in the top row, because otherwise the line of numbers would be too long.

#### Slide 13 -Tekstslide

Question 1: Is a 'zigzag' a good idea or not?

#### Slide 14 -Tekstslide

A zigzag: a good idea? (Why?)
A
no
B
yes

#### Slide 15 -Quizvraag

Solution:

Yes. Because the height only starts at 120 cm.
(By the way: the Solutionsbook does NOT do this!)

#### Slide 16 -Tekstslide

Question 2: What is a good scale for the corresponding Graph? Why?
For the answer see next slide.
timer
0:30

#### Slide 17 -Tekstslide

A good scale for the VERTICAL
AXIS is ....
A
10 cm in one grid
B
20 cm in one grid
C
5 cm in one grid
D
30 cm in one grid

#### Slide 18 -Quizvraag

QUESTION: What is a good scale for the vertical axis
of the corresponding Graph?
SOLUTION: 260 - 120 = 140
140 : 20 = 7 , so if you use as a scale:
20 cm in table = 1 cm in graph, then you need 7 cm.
That's fine.

#### Slide 20 -Tekstslide

FOTOVRAAG !
Now PLOT the GRAPH and send in a picture of your work in next slide. Remember:
1.  a zigzag at height 120 cm
2. scale on vertical axis: 20 cm in 1 cm.
Make your teacher happy: draw a beautiful graph!
Of course: USE A PENCIL + GEO/RULER!

#### Slide 21 -Tekstslide

Send in you graph!

#### Slide 23 -Tekstslide

A few fine points, before you do the Homework:
.                  .               .              .            .            .

#### Slide 24 -Tekstslide

Two in one?!

Sometimes TWO GRAPHS have to be PLOTTED in
ONE coordinate system.
Why?
Think of a good reason.
ANS

#### Slide 25 -Tekstslide

Why 2 graphs in 1 coordinate system?

#### Slide 26 -Woordweb

SOLUTION:
then you can COMPARE both graphs!

#### Slide 27 -Tekstslide

TIP for
making TABLES:
The line of years in the top row could be SHORTER than here.
For example: 0, 6 and 12 years is good enough. So only 3 will do!
All the more because all points lie on a STRAIGHT LINE!

#### Slide 28 -Tekstslide

COMPARING in two examples:
- for number = 0, the green formula
has as outcome 30, the red one 15.
- the point of intersection is (3, 22);
in this point the numbers and amounts for both formulas are the same!

#### Slide 29 -Tekstslide

The next slide is exercise 12.
It is meant to show that:
TWO GRAPHS HAVE TO BE DRAWN IN ONE COORDINATE SYSTEM!
Just look at the next slide, to see what I mean.

#### Slide 31 -Tekstslide

IMPORTANT:
Because two Graphs have to be drawn, also
two Tables have to be made !
How else can we know some points, that lie on the graph?!

#### Slide 32 -Tekstslide

Is the Graph RISING or FALLING?
Two examples:
The graph for the Formula:             60 + time x 2 = amount
is rising, because per step 2 is added to 60.

The graph for the Formula:             60 - time x 2 = amount
is falling, because per step 2 is subtracted from 60.

#### Slide 33 -Tekstslide

Above you first see explained: a rising graph.
Below a falling graph is explained.
Most important are the signs        +  and   -.
The minus sign before the multiplication means a falling graph!
Suppose the minus sign was before 60 it only meant that the graph starts
at a lower point. It says nothing about falling or rising.
Next slide says it in other words.

#### Slide 34 -Tekstslide

Homework time - skip 9, 10 and 11
because we did a lot together.
Do §6.2 now.
Both 12 and 13 contain TWO graphs. So MAKE TWO TABLES then.
Plotting good Graphs, using a pencil and a geo/ruler.
1.make it
2.correct your work with the Solutionsbook