2TH §1.6 Line through two given points.

§1.6
Learning goal:
how to make a formula for a line that passes through two (given) points
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§1.6
Learning goal:
how to make a formula for a line that passes through two (given) points

Slide 1 - Diapositive

Let's do a useful exercise together!
This subject might be pretty difficult.
That's why we do this together, step by step!

Slide 2 - Diapositive

Task: make a linear formula.
Given are two points:
P(10, 6) and Q(18, 30)
You will do similar tasks later. 
Now we tackle this one together!

Slide 3 - Diapositive

First: it helps to make a Sketch!
Without it, the task stays pretty obscure...


Slide 4 - Diapositive

The given points
P(10, 6)  and  Q(18, 30) 
are drawn 
in this coordinate system.

Slide 5 - Diapositive

TASK: calculate the GRADIENT.
ANS (answer it in next slide)


Use the given points,
P(10, 6)  and  Q(18, 30) !

Slide 6 - Diapositive

Gradient is ...
A
5
B
-3
C
1/3
D
3

Slide 7 - Quiz

Solution:
Going from P(10, 6)  to  Q(18, 30) means:
-  going up 30 - 6 = 24 (= vertical increase) 
-  going to the right 18 - 10 = 8 (= horizontal increase)
If we divide the vertical increase by the horizontal increase we get the 
gradient:    24 : 8 = 3 = gradient !


Slide 8 - Diapositive

Slide 9 - Diapositive

TASK 
Find the y - intercept!
There's one problem: you cannot read 
it off! 
So a CALCULATION is needed here!
THERE ARE 2 METHODS FOR FINDING THE Y-INTERCEPT.
Here comes the 1st one.

                    

Slide 10 - Diapositive

Finding the y-intercept following 
Method 1: 
-  we use the general shape of a linear formula: y = ax + b
- we fill in the gradient, that we just calculated:
   y = 3x + b
- to find the y-intercept, we fill in one of the given points;
  see next slide!

Slide 11 - Diapositive

In the formula:   y = 3x + b
we fill in P(10, 6) as follows:
6 = 3    10 + b            Note: the dot means 'times'!
6 = 30 + b
b = -24       We found the value of b, so we found the y-intercept!

Slide 12 - Diapositive

Now we can make the formula complete:
We had y = 3x + b  already.
We just calculated that b = -24
So the formula is:
y = 3x -24                                                     

Slide 13 - Diapositive

2nd Method to find the y-intercept!

Slide 14 - Diapositive

Another way to calculate the Gradient and the
y-intercept !                 With TABLES.
The points P(10, 6) and Q(18, 30) are placed in this table:

Slide 15 - Diapositive

Adding 8  to  x    and
adding  24  to  y,
means the same as:
adding   1  to  x  and
adding  3  to  y !                               That's because  24 : 8 = 3

Slide 16 - Diapositive

Slide 17 - Diapositive

Adding 1 to x means adding 3 to y.
Then the gradient is ..
A
1
B
-3
C
3
D
1/3

Slide 18 - Quiz

Solution: the GRADIENT is:  
                                                      3
because going one place to the right in the graph,
means going 3 places up!

Slide 19 - Diapositive

To find the y-intercept with the table,
we have to find the y coordinate to 0  as x-coordinate:
Try to find the y-intercept!
 So: what has to be filled in 
on the dots?
ANS

Slide 20 - Diapositive


A
-30
B
-24
C
24
D
0

Slide 21 - Quiz

To find the y-intercept with the table,
we have to find the y coordinate to 0  as x-coordinate:
The numbers  1  and  3
have the same ratio as 
-10  and  -30.
So we do 6 -30 = -24
-24 is the y-intercept!

Slide 22 - Diapositive

FORMULA:
y = 3x - 24

Slide 23 - Diapositive

we do 41a together:

So open your Notebook, Then 
write '41' in the margin.
take a pencil and a geo and make the sketch!

timer
1:20

Slide 24 - Diapositive

Solution:

Slide 25 - Diapositive

By answering questions 
43 up to 46
you will again find the 
linear formula for the graph
through two given points!

Slide 26 - Diapositive

Useful advice:
On p.31 you see the METHOD, how to make a linear formula for a line through two points.
USE THIS METHOD all the time, when you have to make a formula!
So for instance for questions:   
43abc      44a      and  46ab         

Slide 27 - Diapositive

Homework:
§1.6 Exercises 43, 45 and 46

Test about chapter 1 on Tuesday 3 October

Slide 28 - Diapositive