# 2TH §9.3 Intersecting lines

Planner Chapter 9 Lineair equations
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Slide 1: Slide
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This lesson contains 34 slides, with interactive quizzes, text slides and 1 video.

Lesson duration is: 50 min

## Items in this lesson

Planner Chapter 9 Lineair equations

#### Slide 1 -Slide

§9.3 Intersecting lines, ....

..... is today's hot dinner!

#### Slide 2 -Slide

9.3 Intersecting lines
When two lines intersect they meet in a point.
Next slide shows this.

#### Slide 4 -Slide

9.3 Intersecting lines
The point of intersection is  (4, 11)
That point has coordinates (x, y)

The two graphs have the same x and y in the point of intersection.

#### Slide 5 -Slide

In the next slide ......
is shown how to put into practice what you have learned in
§9.1 and §9.2!
Solving linear equations turns out to be extremely useful
to calculate the point of intersection of 2 graphs!

#### Slide 6 -Slide

How to CALCULATE the point of intersection of the graphs of two linear formulas ?
You can sometimes READ OFF the point of intersection.

If you have no graph, you have to MAKE AN EQUATION by making the two linear formulas equal to each other.

#### Slide 7 -Slide

How to CALCULATE the point of intersection of the graphs of two linear formulas ?
Solve the equation to find the x-value of the point of intersection.
Formula 1:  y = 1.5x + 5
Formula 2:  y = -x + 15

This is the equation:      1.5x + 5 = -x + 15

For the rest:  see next slides!

#### Slide 8 -Slide

How to calculate the point of intersection of the graphs of two linear formulas ? You learnt this in §9.2 Solving equations!
Formula 1 = Formula 2
you get this equation:                                                                  1.5x + 5 = -x + 15
+ 1x to both sides gives:                                                              2.5x + 5 = 15
-/- 5 on both sides gives:                                                            2.5x = 10
: 2,5 on both sides gives:                                                                   x = 4

#### Slide 9 -Slide

How to calculate the point of intersection of the graphs of two linear formulas ? You learnt this in §9.2 Solving equations!
1.5x + 5 = -x + 15
x = 4
Now fill x = 4 into one of the formulas to calculate y:
y = 1.5 x 4 + 5 = 6 + 5 = 11
so the coordinates of the point of intersection are:  (4,11)

You can check by filling x = 4 into the other formula:
y = -x + 15 = -4 + 15 = 11        gives the same answer, making us happy.

#### Slide 11 -Slide

Let's do exercise 18 together!
+ open your Notebook and take a pen out of your pencilcase
+ Open your Textbook on p.98
+ Have a short look at 18, esp. the GRAPH!
+ Step by step try to do this exercise,

Question 18a:
timer
1:00

#### Slide 14 -Slide

What equation??  Well, this one:

Make it in your Notebook, again.
Use all that you learned in §9.1 and §9.2 now!

Work it out in your Notebook right now!
timer
1:30

#### Slide 15 -Slide

The solution to the equation
5x + 2 = -3x + 20 is ........
41
41
A
9
B
49
C
11
D
241

#### Slide 16 -Quiz

Solution equation:
This is how you are supposed
to have worked out the equation in your
Notebook, just now.
Just like you did in §9.1 and §9.2!

#### Slide 18 -Slide

What x-value?!
Well:  x = 2

Work this out in your Notebook, now!

41
timer
0:40

#### Slide 19 -Slide

Filling in x = 2 1/4 in y = 5x + 2
gives ...............
timer
1:00
A
14
B
13 1/4
C
13 3/4
D
13

Solution:

#### Slide 21 -Slide

So fill in x = 2 1/4 in this formula.
Work it out in your Notebook.
timer
0:45

#### Slide 22 -Slide

Fill in x = 2 1/4 in
y = -3x + 20
A
13 1/4
B
12 1/4
C
12 3/4
D
13.25

Solution:

#### Slide 24 -Slide

Do you get the same result?

#### Slide 25 -Slide

Now try it yourself with:

exercises  19, 21, 22, S19
Later this Lessonup will be carried on for a little while.

#### Slide 26 -Slide

On p.100 you are asked to
MAKE A SKETCH of the GRAPH of a FORMULA.
Making a GRAPH is a lot of work,
making a SKETCH isn't! Let's look at it a bit closer.
WHY all this SKETCHING? You need this in §9.4 !
So LEARNING it NOW helps you doing the next paragraph.

#### Slide 27 -Slide

When asked to MAKE a SKETCH of this FORMULA,
you might wonder:
- where does the sketch go through the VERTICAL AXIS and
- what is the SLOPE (helling) of it?

#### Slide 28 -Slide

SOLUTION
SKETCH:

Another example follows!

#### Slide 29 -Slide

MAKE a SKETCH for this FORMULA:

- where does it go
through the VERTICAL AXIS and
- what is the SLOPE?

#### Slide 30 -Slide

MAKE a SKETCH for this FORMULA:

#### Slide 31 -Slide

Theory
+  y-intercept tells you where the line intercepts the y-axis
+  gradient tells you whether the line is
a.  rising (if gradient is positive)
or it is
b.  falling (if gradient is negative)

#### Slide 33 -Video

Homework time
+ now do §9.3
+ Do Exercises:    19, 21, 22, S19