# 2Tvwo 9.3 Intersecting lines (1)

§9.3 Intersecting lines, ....

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

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Slide 1: Slide
WiskundeMiddelbare schoolvwoLeerjaar 2

This lesson contains 40 slides, with interactive quizzes, text slides and 1 video. Lesson duration is: 50 min

## Items in this lesson

§9.3 Intersecting lines, ....

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

#### Slide 1 -Slide

First a question on the ENTRANCE TICKET you just did.

#### Slide 2 -Slide

This is how I did on the ET:
A
B
good
C
moderate
D
excellent

#### Slide 3 -Quiz

9.3 Intersecting lines
When two lines intersect they meet in a point.
Next slide shows this. The point of intersection (= p.o.i.) is  (4, 11)
That point has coordinates (x, y)
x is the value on the horizontal axis
and y is the value on the vertical axis.
so
for this particular value of x both lines have the same value for y.
You could say they are equal to each other.

#### Slide 5 -Slide

In the next slide ......
is shown how to put into practice what you learned in
§9.1 and §9.2!
Solving linear equations turns out te 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.

Solve the equation to find the x-value of the point of intersection.
e.g. with formulas                           y= 1.5x + 5         and              y = -x + 15
you get this equation:                           1.5x + 5 = -x + 15
For the rest:  see next slide!

#### Slide 7 -Slide

How to calculate the point of intersection of the graphs of two linear formulas ? You learnt this in §9.2 Solving equations!
you get this equation:                                                                  1.5x + 5 = -x + 15
adding 1x to both sides gives:                                                  2.5x + 5 = 15
subtract 5 from both sides gives:                                           2.5x = 10         so 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 9 -Slide

Let's do exercise 20 together!
+ open your Notebook and take a pen out of your pencilcase
+ Open your Textbook on p.97
+ Have a short look at 20, esp. the GRAPH!
+ Step by step try to do this exercise,

timer
0:45

#### Slide 12 -Slide

Solution:
20a y = -3x + 20 corresponds to
graph 1, because this graph is falling and
this formula has -3 as gradient.
A negative gradient means a falling graph!

timer
1:00

#### Slide 16 -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 17 -Slide

The solution to the equation
5x + 2 = -3x + 20 is ........
41
41
A
2
B
4 1/2
C
- 2 1/41/4
D
2 1/4

#### Slide 18 -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 20 -Slide

What x-value?!
Well:  x = 2

Work this out in your Notebook, now!

41
timer
0:40

#### Slide 21 -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 23 -Slide

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

#### Slide 24 -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:

timer
0:45

#### Slide 28 -Slide

exercise 20, once more, in full:
y= 5x + 2 and y = -3x +20
a)    graph 1 starts high and gets lower so y = -3x + 20
b)    when they intersect they are equal so 5x + 2 = -3x + 20
c)     solving the equation :
first add 3x to both sides giving             8x + 2 = 20
then subtracting 2 from both sides      8x = 18
then dividing both sides by 8  gives         x = 2.25
d)        fill x= 2.25 into y = 5x + 2  gives y = 5 x 2.25 + 2 = 11.25 + 2 = 13.25
e)       fill x= 2.25 into y = -3x + 20 gives y = -3  x  2.25 + 20 = -6.75 + 20 = 13.25
f)        yes, they both give y=13.25 when x= 2.25

#### Slide 29 -Slide

Now try it yourself with:

exercises  21   t/m   24
Later this Lessonup will be carried on for a little while.

#### Slide 30 -Slide

On p.98 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 31 -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 32 -Slide

SOLUTION
SKETCH:

Another example follows!

#### Slide 33 -Slide

MAKE a SKETCH for this FORMULA:

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

#### Slide 34 -Slide

MAKE a SKETCH for this FORMULA:

#### Slide 35 -Slide

Theory on page 98
+  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 37 -Slide

HINTS to. 24a SKETCHING the graphs:
+  you need to see where they intersect the
y-axis, and
+  you need to see what the gradient is.

#### Slide 39 -Video

Homework time
+ now do §9.3
+ make:    21   t/m   24
+ send in slides of your work