2TH/vwo §1.3 Making linear formulas

§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.
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§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.

Slide 1 - Diapositive

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!

Slide 2 - Diapositive

Slide 3 - Diapositive

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.

Slide 4 - Diapositive

The right formula is:
timer
0:20
A
c = 15b + 5
B
15 + 5b = c
C
c = 15 + 5b
D
b = 15c + 5

Slide 5 - Quiz

The right answers were:

B        15 + 5b = c    and
C         c = 15 + 5b

Slide 6 - Diapositive

Slide 7 - Diapositive

3rd:   Now we have a graph of a straight line.
How to make a linear formula?   Next slide shows you how!            

Slide 8 - Diapositive

The next slide shows you


The next slide describes which steps were taken.

Slide 9 - Diapositive

This is what has been done:
 15.06.28

Slide 10 - Diapositive

Task:
You make 
the formula!
STEP 1:
Choose the correct
 points in the 
next slide.

Slide 11 - Diapositive

Correct points are:
A
(15, 0)
B
(0, 5)
C
(0, 15)
D
(5, 0)

Slide 12 - Quiz

STEP 2:
Calculate the
gradient.

timer
0:30

Slide 13 - Diapositive

timer
0:15
Key in the gradient.

Slide 14 - Carte mentale

STEP 2:
Solution:
the gradient =
-15 / 5 = -3
A negative gradient, 
because the graph is falling!

Slide 15 - Diapositive

STEP 3:
Read off the
y-intercept.
ANS (= answer in 
the next slide)

Slide 16 - Diapositive


A
5
B
15
C
(0, 15)
D
(15, 0)

Slide 17 - Quiz

STEP 3:
Solution:
15 is the y-intercept.
Not (0, 15), because 
it is a NUMBER and 
not a POINT!

Slide 18 - Diapositive

And the 
FORMULA is ......
Choose the
good one.
ANS

Slide 19 - Diapositive

The formula is:
A
y = -15 + 3x
B
y = 15 - 3x
C
y= -3x + 15
D
y = 3x - 15

Slide 20 - Quiz

And the 
FORMULA is ......
y = -3x + 15  or
y = 15 -3x

Slide 21 - Diapositive

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

Slide 22 - Diapositive