# 1TH/vwo §6.2 Graphs from formulas

1TH/vwo §6.2 Graphs from formulas
(you may skip 9, 10, 11 as we 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.
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Slide 1: Slide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 1

This lesson contains 33 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

## Items in this lesson

1TH/vwo §6.2 Graphs from formulas
(you may skip 9, 10, 11 as we 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 -Slide

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 -Slide

7
This is the Theory.
Next slide shows us an example.

5

ANS!

#### Slide 4 -Slide

Steps of 60 is fine, because ...
A
you have to put 300 on the 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 -Quiz

6
Points of attention:
+ 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 -Slide

What to do first, before plotting the graph?

First you ....

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

#### Slide 9 -Slide

You may skip exercises 9, 10 and 11.
Now:
COPY and MAKE this task in your Notebook,  by copying and filling in the Table above!

timer
2:00

#### Slide 10 -Slide

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 12 -Slide

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

#### Slide 13 -Slide

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

#### Slide 14 -Quiz

Solution:

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

#### Slide 15 -Slide

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

#### Slide 16 -Slide

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 18 -Slide

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 19 -Slide

Send in you graph!

#### Slide 21 -Slide

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

#### Slide 22 -Slide

Here are the points again. Now it offers more content!
Sometimes TWO GRAPHS have to be PLOTTED in
ONE coordinate system.
Why?
Think of a good reason.
ANS

#### Slide 23 -Slide

TIP for
making TABLES:
The number of years could be LESS 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 24 -Slide

Why 2 graphs in 1 coordinate system?

#### Slide 25 -Mind map

SOLUTION:
then you can COMPARE both graphs!

#### Slide 26 -Slide

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 27 -Slide

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 29 -Slide

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 30 -Slide

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 31 -Slide

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 32 -Slide

Homework time - skip 9, 10, 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
3.take pics and
4.send them in in GC