# preparing for the formative assessment

Good morning!
Schedule:
• Revise chapter 3
• Practise (formative assessment)
1 / 32
Slide 1: Slide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 32 slides, with interactive quizzes and text slides. Lesson duration is: 40 min

## Items in this lesson

Good morning!
Schedule:
• Revise chapter 3
• Practise (formative assessment)

#### Slide 1 -Slide

What paragraph do you find the most difficult?
3.1 The graph of a linear function
3.2 Finding the equation of a line
3.3 linear relationships
3.4 The balance method
3.5 Solving equations
3.6 Applying equations

#### Slide 2 -Poll

3.1 The graph of a linear function

How to draw a graph of a linear function in the coordinate plane
1. Make a table with at least 2 points.
2. Plot these points in the coordinate plane.
3. Draw a line through these points.
4. Don't forget to write the formula next to your graph!

#### Slide 3 -Slide

Example
Draw the graph of y = -3x + 2.
1.

x
0
1
y
2
-1
For x = 0
y = -3 · 0 + 2 = 0 + 2 = 2
y = 2
For x = 1
y = -3 · 1 + 2 = -3 + 2 = -1
y = -1
This gives us the points:
(0,2) and (1,-1)

#### Slide 4 -Slide

Example
2. Plot (0,2) and (1,-1)

#### Slide 5 -Slide

Example
2. Plot (0,2) and (1,-1)
3. Draw a line through (0,2) and
(1,-1)

#### Slide 6 -Slide

Example
2. Plot (0,2) and (1,-1)
3. Draw a line through (0,2) and
(1,-1)
4. Write the formula next to the
graph!!

#### Slide 7 -Slide

3.1 The graph of a linear function
How to check if a point is on a line
To check if point (x,y) in on a line you fill in the x-coordinate in the formula of the line and see if the answer matches the y-coordinate.

If the answer and the y-coordinate are the same, the point is on the line.

#### Slide 8 -Slide

Example
Calculate wether points A(9,15) and B(-2,-8) are on line y = 2x - 3
Check point A:
Filling in x = 9 in y = 2x-3 gives:
y = 2 · 9 - 3 = 18 - 3 = 15
Check point B:
Filling in x = -2 in y = 2x-3  gives:
y = 2 · -2 - 3 = -4 - 3 = -7
Point A(9,15) is on the line
Point B(-2,-8) is not on the line

#### Slide 9 -Slide

3.2 Finding the equation for a line

The formula for a linear relationship between x and y in an equation in the form
y = ax+b

Going 1 to the right means going a up
The line has y-intercept (0,b)

#### Slide 10 -Slide

y = 2x -3
Going 1 to the right means going 2 up
This line has y-intercept (0,-3)

#### Slide 11 -Slide

how to find the equation of a line
1. Assume y = ax + b
2. Find the y-intercept. This is (0,b)
3. Pick two grid points on the line.

4. Write down the equation.

a=runrise

a = .....

What is the
y-intercept?
A
(0,1)
B
(1,0)
C
(0,-1)
D
(-1,0)

#### Slide 14 -Quiz

What is the
equation of this line?
a = -2
y-intercept = (0,-1)

#### Slide 15 -Open question

Equations of parallel lines
Lines with the same gradient are parallel
Parallel lines have the same gradient

Line l and k both have gradient -2
Line l and k are parallel

Line m is not parallel to line l or k

#### Slide 16 -Slide

3.3 linear relationships
How to find the equation of a line where the axis have different lables than x and y.

The horizontal axis is labelled p and the vertical axis is labelled N

The equation is in the form:
N = ap + b

#### Slide 17 -Slide

Find the equation

1. The equation is in the form
N = ap + b
2. The line goes through (0, -80), so b = -80
3.
4.  N = ap + b
b = -80 and a = 5 so
N = 5p - 80
a=runrise=20100=5

#### Slide 18 -Slide

The sum graph

To draw the sum graph of two graphs you need two points of this graph.
You can find these points in two way:
1. By adding the y-values of the two graphs with the same x-value
2. By finding the points directly above the x-intercepts of the two graphs
You don't need to know this for the test!

#### Slide 19 -Slide

Given are the lines f and g with equations f: y = -2x + 6 and
g: y = 3x - 2

f.

g.

f + g.

Two points on the sum graph are :
(0,4) and (1,5)
x
0
1
y
6
4
x
0
1
y
-2
1
x
0
1
y
6 + -2
4 + 1
You don't need to know this for the test!

#### Slide 20 -Slide

You see the sum graph of line f and g. In what order would you do these steps to find the sum graph?
You don't need to know this for the test!
Step 1: find the x-intercept
Step 2:
Find the y-values directly above the y-intercepts
Step 3: Draw a line through the new points

#### Slide 21 -Drag question

1. substracting y-values
Given are the lines f and g with equations f: y = -2x + 6 and
g: y = 3x - 2

f.

g.

f - g.

Two points on the sum graph are :
(0,8) and (1,3)
x
0
1
y
6
4
x
0
1
y
-2
1
x
0
1
y
6 - -2
4 - 1
The difference graph
You don't need to know this for the test!

#### Slide 22 -Slide

1. finding the y-values with the x-intercepts

Step 1: Find the x-intercept with the same y-value as the intersection point

Step 2: Find the x-intercept of the line you are substracting

Step 3: Find the point with the same x-value as the point you found in step 2 on the other line (in this case line f)

Step 4: Draw a line through the two points from step 1 and step 3
In this case we are trying to find lin f-g
So we are looking for the x-intercept of line g
You don't need to know this for the test!

#### Slide 23 -Slide

When you have an equation and you want to find the solution for x:

You can Add or Substract the same number on both sides
You can multiply or divide by the same number on both sides

Example:

5x + 7      = 32
-7          -7
5x + 7 -7 = 32 -7
5x + 0      = 25
5x              = 25
:5                   :5
5x:          = 25:5
x                  = 5
3.4 The balance method
We always want the variables on the lefthand side,
That's why we try to remove the 7 from the LHS first

#### Slide 24 -Slide

Try it yourself!

1. -7x + 3 = 24                                                       2. -5 + 6x = 37

Try to remove the 3 on the left hand side first.
We only want x on the left hand side!
Hint
Try to remove the -5 on the left hand side first.
We only want x on the left hand side!
Hint

#### Slide 25 -Slide

Solutions
1. -7x + 3        = 24                                             2. -5 + 6x         = 37
- 3     - 3                                                        +5              +5
-7x + 3 - 3 = 24 - 3                                            -5 + 5 + 6x = 37 + 5
-7x + 0       = 21                                                    0 + 6x           =  42
-7x               = 21                                                    6x                  = 42
:-7                     :-7                                                 :6                        :6
-7x : -7          = 21:-7                                             6x : 6            = 42 : 6
x                     = -3                                                   x                    = 7

#### Slide 26 -Slide

3.5 Solving equations
In what order should you solve an equation (with brackets)?
1.
2.
3.
4.
If there are brackets, multiply them out.

Simplify the LHS and the RHS if needed.

Move all the terms with a variabel to the LHS and move all the terms without a variabel to the RHS.
Divide by the number in front of the variabel

#### Slide 27 -Drag question

3.5 Solving equations
Equations with fractions
When you want to change a fraction into a whole number, you multiply the fraction by it's denominator because:

so what should
we do when
4314=412=3
53x=6
4/1 = 4
?

#### Slide 28 -Slide

How would you solve
?
53x=6

#### Slide 29 -Open question

3.6 Applying equations
You can solve many problems using an equation!!

Problem:

In 4 years I will be 5 times as old as I was 16 years ago. How old am i now?
I want to know my age right now so we will call this x. Right now I am x years old.

How old am I in 4 years?
How old was I 16 years ago?
What is equal to my age 16 years ago times 5?

#### Slide 30 -Slide

3.6 Applying equations
You can solve many problems using an equation!!

Problem:

In 4 years I will be 5 times as old as I was 16 years ago. How old am i now?
Right now my age is x
How old am I in 4 years? x + 4
How old was I 16 years ago?  x - 16
What is equal to my age 16 years ago times 5? (x - 16) · 5 = x + 4

Now solve for x to find my age!

#### Slide 31 -Slide

What can I work on right now?
Mixed exercises: p. 122-123

Diagnostic test: p.126-127

Revision: p. 128-129