Lesson 2: Patterns with constant relationships

Lesson 2: Patterns with constant relationships

VARIABLES

Variables are values that can change. The independent variable is the value that is shown on the ����-axis. It is independent from the dependent variable and is not affected by other variables. For example, time is always an independent variable. It changes as time passes, without it being affected by something else or being dependent on something.

The dependent variable is the value that is shown on the ����-axis. It is determined by the independent variable.

TYPES OF VARIABLES

Discrete values consist of whole numbers, for example, the number of people standing in a queue, the number of apples in a bag, days of the week. These are values that are not used as fractions in context. Discrete values are indicated by points (dots) which can be connected by dotted lines.

Continuous values consist of fractions (common or decimal fractions), for example, length, weight, age. Continuous values are indicated by solid lines because the values between the points are also included.

Increasing relationships exist when the independent and dependent variables both increase.

���� =������������ (���� >1)

Decreasing relationships exist when the independent variable increases and the dependent variable decreases.

Constant or fixed relationships occur when the dependent variable (����) remains constant and the independent variable (����) increases.

EXAMPLE

The Naidoo family wants to go on holiday in Cape Town.

They receive two quotations to rent apartments for 8 people.

• Apartment 1: R1 500,00 per day • Apartment 2: R1 800,00 per day

We can represent the above information with a: • table • formula • graphical representation

Table

Number of people 0 1 2 3 4 5 6 7 8

Apartment 1 1 500 1 500 1 500 1 500 1 500 1 500 1 500 1 500 1 500

Apartment 2 1 800 1 800 1 800 1 800 1 800 1 800 1 800 1 800 1 800

Formula

Apartment 1 = 1 500 Apartment 2 = 1 800

Graphical representation