1TH/vwo §6.2 Graphs from formulas

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

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.

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

7

This is the Theory.

But HOW do you do these steps?!

Next slide shows us an example.

5

ANS!

Steps of 60 is fine, because ...

1. you have to put 300 on the vertical axis; then you need 300 : 60 = 5 cm.
2. the time goes from 0 to 5
3. the distances go up by 60 all the time
4. there is no zigzag needed

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.

This is Task A.

Question about this task:

What to do first, before plotting the graph?

Answer in next slide.

First you ....

Solution:

First you ...

MAKE A TABLE !

As follows:

Task A.

 COPY this task in your Notebook,  

the FILL IN the Table above!

COMPARE your TABLE with the one below:

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.

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

A zigzag: a good idea? (Why?)

1. no
2. yes

Solution:

Yes. Because the height only starts at 120 cm.

(By the way: the Solutionsbook does NOT do this!)

Question 2: What is a good scale for the corresponding Graph? Why?

THINK about this for half a minute.

 For the answer see next slide.

A good scale for the VERTICAL
AXIS is ....

1. 10 cm in one grid
2. 20 cm in one grid
3. 5 cm in one grid
4. 30 cm in one grid

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.

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!

Send in you graph!

A few fine points, before you do the Homework:

.                  .               .              .            .            .

Two in one?!

Sometimes TWO GRAPHS have to be PLOTTED in 

ONE coordinate system.

Why?

Think of a good reason.

ANS

Why 2 graphs in 1 coordinate system?

SOLUTION:

then you can COMPARE both graphs!

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!

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!

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.

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?!

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.

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.

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