1718 WH3X CH4 Lesson 1

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

CH4 Types of Relations

                                          Linear Relation (& Directly Proportional)
                 Fractional Formulas (& Inversely Proportional Relations)
Power Formulas                         Square root Formulas
              Quadratic Relations                      Exponential Relations

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Solving linear equations
Linear formulas
Exponential formulas

Solving linear equations

You can solve linear equations with the balance method or sometimes with the cards method.
The balance method means you can add/subtract the same thing on both sides of the = sign and that you can multiply/divide by the same number on both sides of the = sign.
Sometimes you have to remove brackets first.
The cards method lets you place a "card" on the part containing the variable, then you work out what the value of the "card" is.

Example cards method
5t + 7 = 10

5t = 3

t=0.6

• place a card on "5t"

"3" + 7 = 10

• place a card on "t"

5 x "0.6" = 3

Solve the equation
3a + 8 = 20

example balance method
3(2a - 4) = 2a - 2

6a - 12 = 2a - 2

4a - 12 = -2

4a = 10

a = 2.5

• remove brackets

• subtract 2a on both sides

• add 12 on both sides

• divide by 4 on both sides
  

Solve the equation
5a + 2 = 3a - 8

Linear formulas

General form:
(a is called the gradient and b is called the y-intercept)

Graph: straight line (increasing or decreasing)

Is this a linear formula?
y = 5 - 2x

1. yes
2. no

Is this a linear formula?
y = 3x

1. yes
2. no

Making a linear formula for a line
through two given points

1) Write down the general form of a linear formula: y = ax + b
2) Calculate the gradient using the formula:

3) Fill in the gradient (a) in the general formula
4) Fill in the x and y coordinate of one of the two points in the general formula and calculate the y-intercept (b).
5) Write down the linear formula

Example

A line passes through point A(3, 5) and B(7, -11).
Give a formula for this line.

1) Write down the general form of a linear formula

What is the general form of a linear formula?

Example

A line passes through point A(3, 5) and B(7, -11).
Give a formula for this line.

2) Calculate the gradient using the formula:

What is the correct calculation for the gradient of the line through A(3,5) and B(7,-11)?

1. ​5−−11​​3−7​​=​16​​−4​​=−0.25
2. ​−11−5​​7−3​​=​−16​​4​​=−0.25
3. ​3−7​​5−−11​​=​−4​​16​​=−4
4. ​7−3​​−11−5​​==​4​​−16​​−4

Example

A line passes through point A(3, 5) and B(7, -11).
Give a formula for this line.

3) Fill in the gradient (a) in the general formula

Example

A line passes through point A(3, 5) and B(7, -11).
Give a formula for this line.

4) Fill in the x and y coordinate of one of the two points in the general formula and calculate the y-intercept (b).

Solve the equation
5 = -4 x 3 + b

Example

A line passes through point A(3, 5) and B(7, -11).
Give a formula for this line.

5) Write down the linear formula

Exponential formulas

General form:
(g is called the growth factor and b the initial amount)

Table:                                                here b = 40 (value of h at t = 0)                                                              and g = 0.5  (value you multiply h
                                                             with when t  increase by 1)                          

Exponential formulas

example:
What are the initial amount and growth factor for this table?
What is the corresponding formula?
(Quiz answers on next slide)

What formula corresponds to the table?

1. n=6t+2
2. n=2+6​t​​
3. n=2⋅6​t​​
4. n=2⋅6t

Homework Tuesday

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