# 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 33 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

9.3 Intersecting lines
When two lines intersect they meet in a point.
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 3 -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 4 -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 can 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 equation:                           1.5x + 5 = -x + 15

#### Slide 5 -Slide

How to calculate the point of intersection of the graphs of two linear formulas ?
you get equation:                                                           1.5x + 5 = -x + 15
add 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 other formula y = -4 + 15 = 11 which gives the same answer.

#### Slide 6 -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,
+ Answering all the questions on LessonUp.

timer
0:45

#### Slide 9 -Slide

Which formula corresponds to graph 1?
Explain why.
A.  y = -3x + 20, because it is falling    B.  y = 5x + 2, because it is rising
C.  y = 5x + 2, because it is falling         D.  y = -3x + 20, because it is rising

#### Slide 10 -Slide

Which formula? Why?
A
y = -3x + 20; falling
B
y = 5x + 2; rising
C
y = 5x + 2; falling
D
y = -3x + 20; rising

timer
1:00

#### Slide 14 -Slide

What equation??  Well, this one:

Work it out in your Notebook right now!
timer
1:00

#### Slide 15 -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 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:

timer
0:45

#### Slide 26 -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 27 -Slide

After this LessonUp  try it yourself with:

Do:  exercises  21   t/m   24
For 21:
STUDY the METHOD above
the task! Then take the 4 steps they
explain here yourself.

#### Slide 28 -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 29 -Slide

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

#### Slide 30 -Slide

optional:
For a fine (Dutch) explanation from the