# 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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Slide 1: Slide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 28 slides, with interactive quizzes and text slides.

Lesson duration is: 45 min

## Items in this lesson

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

#### Slide 1 -Slide

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 -Slide

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 -Slide

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

#### Slide 4 -Slide

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

#### Slide 5 -Slide

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

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

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 9 -Slide

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 -Slide

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 -Slide

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 -Slide

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 -Slide

2nd Method to find the y-intercept!

#### Slide 14 -Slide

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 -Slide

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 17 -Slide

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 -Slide

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

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!

FORMULA:
y = 3x - 24

#### Slide 23 -Slide

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

Solution:

#### Slide 25 -Slide

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

#### Slide 26 -Slide

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 -Slide

Homework:
§1.6 Exercises 43, 45 and 46

Test about chapter 1 on Tuesday 3 October