2TH/vwo §1.3 Making linear formulas

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

§1.3 Making linear formulas

Goal of this paragraph:

How to make a formula for a straight line that describes a relation between x and y.

1st           a freshen up:

The formula for a straight line is called a LINEAR FORMULA.

The graph for the formula s = 15 - 3a is a straight line.

This is taken from §1.1 Linear relations.

Next slide shows you the graph too!

2nd:         we make an example of a linear formula:

-  Suppose we, as a class and a teacher, go on a rowing trip on the 

    Ijsselmeer.

-  The fixed amount (the money we have to pay, no matter how many boats are hired) is 15 euros.

-  The number of boats we hire we call b.

-  Every boat costs 5 euros.

-  The total cost for the trip we call c.

-  In the next slide CHOOSE the RIGHT FORMULA for this trip.

The right formula is:

1. c = 15b + 5
2. 15 + 5b = c
3. c = 15 + 5b
4. b = 15c + 5

The right answers were:

B        15 + 5b = c    and

C         c = 15 + 5b

3rd:   Now we have a graph of a straight line.

How to make a linear formula?   Next slide shows you how!            

The next slide shows you

The next slide describes which steps were taken.

This is what has been done:

 15.06.28

Task:

You make 

the formula!

STEP 1:

Choose the correct

 points in the 

next slide.

Correct points are:

1. (15, 0)
2. (0, 5)
3. (0, 15)
4. (5, 0)

STEP 2:

Calculate the

gradient.

Key in the gradient.

STEP 2:

Solution:

the gradient =

-15 / 5 = -3

A negative gradient, 

because the graph is falling!

STEP 3:

Read off the

y-intercept.

ANS (= answer in 

the next slide)

1. 5
2. 15
3. (0, 15)
4. (15, 0)

STEP 3:

Solution:

15 is the y-intercept.

Not (0, 15), because 

it is a NUMBER and 

not a POINT!

And the 

FORMULA is ......

Choose the

good one.

ANS

The formula is:

1. y = -15 + 3x
2. y = 15 - 3x
3. y= -3x + 15
4. y = 3x - 15

And the 

FORMULA is ......

y = -3x + 15  or

y = 15 -3x

Homework:

+  When making formulas, write down the 4 steps you learnt!

+   Vwo  choose the Standard or Challenge  path

+  Check your Homework with the Solutionsbook and

+  Make some pictures of it and send them in, in GC