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2TH/vwo §1.5 Line through two given points.
§1.5
Learning goal:
how to make a formula for a line that passes through two (given) points
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Slide 1:
Slide
Wiskunde
Middelbare school
havo, vwo
Leerjaar 2
This lesson contains
28 slides
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interactive quizzes
and
text slides
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Lesson duration is:
45 min
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Items in this lesson
§1.5
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 is found pretty difficult, sometimes.
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) !
Slide 6 - Slide
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 - Slide
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 16 - Slide
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
Slide 20 - Slide
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 - Slide
FORMULA:
y = 3x - 24
Slide 23 - Slide
we do 33a together:
So open your Notebook, Then
write '33' in the margin.
take a pencil and a geo and make the sketch!
timer
1:20
Slide 24 - Slide
Solution:
Slide 25 - Slide
By answering questions
33b, c, d, e, f and g
you will again find the
linear formula for the graph
through two given points!
Slide 26 - Slide
Useful advice:
On p.27 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:
35a, b, c 36a and 37d
Slide 27 - Slide
Homework:
§1.5, not 32, 34 and 38.
By the way, later on in this lesson I will give you a little more advice about the exercises.
Slide 28 - Slide
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