1TTO §6.2 Graphs from formulas PTI Apr24

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

§6.2 Graphs from formulas

(you may skip some exercises 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.

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.

Next slide shows us an example.

> First make a table => variable in top row

                                                 outcome (distance) bottom row

time
distance

5

ANS!

Steps of 60 are fine, because ...

1. you have to put 300 on the 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:

+ 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.

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!

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: a Solutionsbook may 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.

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!

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

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!

SOLUTION:

then you can COMPARE both graphs!

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!

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