2TH §9.3 Intersecting lines

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Planner Chapter 9 Lineair equations

§9.3 Intersecting lines, ....

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

9.3 Intersecting lines

When two lines intersect they meet in a point. 

Next slide shows this. 

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.

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!

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.

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!

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

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.

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,

+ Answering all the questions  in your Notebook.

Question 18a: 

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!

The solution to the equation
5x + 2 = -3x + 20 is ........

​4​​1​​

​4​​1​​

1. 9
2. ​4​​9​​
3. 11
4. 2​4​​1​​

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!

What x-value?!

Well:  x = 2         

  

Work this out in your Notebook, now!      

​4​​1​​

Filling in x = 2 1/4 in y = 5x + 2
gives ...............

1. 14
2. 13 1/4
3. 13 3/4
4. 13

Solution:

So fill in x = 2 1/4 in this formula.

Work it out in your Notebook.

Fill in x = 2 1/4 in
y = -3x + 20

1. 13 1/4
2. 12 1/4
3. 12 3/4
4. 13.25

Solution:

Do you get the same result?

Now try it yourself with:

 exercises  19, 21, 22, S19

Later this Lessonup will be carried on for a little while.

A little more about §9.3

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.

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?

SOLUTION

SKETCH:  

Another example follows!  

MAKE a SKETCH for this FORMULA:

Again we wonder about:

- where does it go

   through the VERTICAL AXIS and

- what is the SLOPE?

MAKE a SKETCH for this FORMULA:

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)

Homework time

+ now do §9.3 

+ Do Exercises:    19, 21, 22, S19

+ Upload copies of your work in Classroom

+ enjoy your day!