2TH Ch 1 TOTALLY!

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

We are going on a trip. Get aboard!

A trip through Book 2A VWO

Ch 1 Linear formulas!

Want to do well on the Test?

Be ready and participate.

You can learn a lot!

A. Have a good look at this table. Is this a linear relation?

B. Answer the question on the following slide!

C. Choose the best answer.

T IN SECONDS 0 10 20 40 50
HEIGHT IN M 30 45 60 90 105

1. Linear.
2. Directly proportional.
3. Linear nor directly proportional.
4. Both.

SOLUTION:

At first it seems  linear, but is it, really?

The height goes up by 15 m all the time.

However, the time goes up by 10 seconds, except for one time, when it goes up by 20. So it is linear, indeed!! 

Choose right or wrong:

1. A linear formula is also directly proportional.
2. A linear formula is sometimes directly proportional.
3. A linear formula is never directly proportional.
4. Linear and directly proportional mean the same.

Directly proportional:

In the table you see that if x is 

done times 2 then also y is done

times 2. Or both times 3; that works too!

The graph is a straight line that goes through the origin.

All this makes the relation between x and y directly proportional.

A directly proportional formula has no y-intercept.

1. True.
2. False.

Explanation:

A directly proportional formula has 0 as y-intercept!

For example:

y = -5x + 0, which is the same as

y = -5x, is a directly proportional formula.

The reason for this: the graph is a straight line, that goes through (0,0).

1. The formula is: H = 15T
2. The formula is: T = 1.5H
3. The formula is: H = 1.5T + 30
4. The formula is: 30 + 1.5H = T

Make a formula for the graph!

Choose the right formula:

1. y = 3x + 4
2. y=−​3​​1​​x+4
3. y=​3​​1​​x+4
4. y = -3x + 4

Answer and explanation.

Below you see the steps you have to take on the test, when making a formula is asked.

1. make a table:

2.  for every horizontal step the graph goes DOWN 3 steps,

    so the gradient is -3

3. the graphs intersects the y-axis at the height 4,  so the y-intercept is 4

4.  So: the formula is:   y = -3x + 4,  or    y = 4 - 3x, or:     -3x + 4 = y   

Key in the formula that corresponds to this graph on the next slide.

What is the right formula?

If x goes 3 steps to the right, then y goes up only 1 step.

So if x goes 1 step to the right, then y goes up 

This means that the gradient is           The formula is:       y =     x -1

​3​​1​​

​3​​1​​

​3​​1​​

Next slide shows a mysterious drawing.

If you know who drew this, then key in the name of the artist.

The artist is ...

His name is: Maurits Escher.

Here's another of his drawings,

 or painting or .... whatever!

1. y = -8x + 1
2. y = 1/8 x + 1
3. y = 8x
4. y = 1/8 x - 1

Explanation formula:

1. make a table:

2. The gradient is 1/8, because in 1 horizontal step the graph goes up 1/8 grid

3. The y-intercept is -1 (read off)

4. Fill in the numbers 1/8 and -1 in the right places and you get:

y = 1/8 x - 1

The graph for y = -3 + 5x is

1. a straight horizontal line
2. a straight rising line
3. a vertical line
4. a straight falling line

Does (-12,-3) lie on the graph for
y = 2x + 21 ?

1. Yes, it does.
2. No, it does not.

Explanation:

Let us fill in (-12, -3) in y = 2x + 21.       As follows:

X = -12 and y = -3

The new equation becomes:

-3 = 2 x -12 + 21  Does this check out?

-3 = - 24 + 21

-3 = -3  Yes this checks out, so: (-12, -3) lies on the line!

Make a linear formula for a vertical line through point (-5, -7)

1. y = -7
2. x = -7
3. y = -5
4. x = -5

All points on the vertical line through (-5, -7) 

have the same x coordinate:  -5.

That's why the formula is:

x = -5

Make a linear formula for a horizontal line through point (-5, -7)

1. x = -7
2. x = -5
3. y = -5
4. y = -7

All points through (-4, -7) have the same y coordinate:  -7

That's why the formula is:

y = -7

Mention something you've learnt this lesson.

If you don't know enough about formulas for horizontal and vertical lines, then Study the Theories on p.15 and 16 from §1.2 closely:

Now the VERTICAL line's formula:

After all this.....

You will have learnt something for the coming test,

to say the least.

Homework time

Make p.36-38:

E1 t/m E8

That's all, folks!