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
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

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

Lesson duration is: 45 min

Items in this lesson

§1.5
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

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

ANS (answer it in next slide)

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

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

Slide 9 -Slide

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 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

means the same as:
adding  3  to  y !                               That's because  24 : 8 = 3

A
1
B
-3
C
3
D
1/3

Slide 18 -Quiz

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 33a together:

write '33' in the margin.
take a pencil and a geo and make the sketch!

timer
1:20

Solution:

Slide 25 -Slide

33b, c, d, e, f and g
you will again find the
linear formula for the graph
through two given points!