2Tvwo 9.3 Intersecting lines (1)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§9.3 Intersecting lines, ....

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

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.

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!

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

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.

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.

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

Key in your answer in the next slide!

Which formula? Why?

1. y = -3x + 20; falling
2. y = 5x + 2; rising
3. y = 5x + 2; falling
4. y = -3x + 20; rising

What equation??  Well, this one:

Work it out in your Notebook right now!

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

​4​​1​​

​4​​1​​

1. 2
2. 4 1/2
3. - 2 1/41/4
4. 2 1/4

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:

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

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.

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)

Something about  24 ......

HINTS to SKETCH the graphs: 

+  you need to see where they intersect the 

         y-axis, and 

+  you need to see what the gradient is. 

optional:

For a fine (Dutch) explanation from the 

WiskundeAcademie,

use this link:

https://youtu.be/M_rHguElNxg

Homework time

+ now do §9.3 

+ make:    21   t/m   24

+ send in slides of your work

+ enjoy your day!