Topics covered within this unit: 9.1 Linear patterns in context 9.2 Solving basic linear equations
9.3 Solving more complicated linear equations
9.4 Creating and solving linear equations
9.5 Introduction to functions 9.6 Linear functions
9.7 Solving linear relations using multiple representations
The Learning Outcomes covered in this unit are contained in the following sections:
AF.1a AF.1b AF.1c AF.2a AF.2b AF.2c AF.4a AF.7a
Key words Equation
Equate
Linear equation Function Couple Domain Range Codomain Linear function
In Unit 7, we learned how to represent a linear pattern using a table or a graph. This is an essential skill, but sometimes it is easier to represent a pattern by developing a formula.
A formula is a rule or fact written with mathematical symbols. It usually has an equals sign (=) and special symbols (usually letters) to represent variables.
Let’s consider the following situation.
Jim is starting a new fi tness regime. He is planning on doing a particular exercise every day, starting with 5 minutes the fi rst day and increasing the length of time spent at the exercise by 2 minutes each day.
Solving linear relations
Something to think about …
Sophie was given a money box by her dad for her birthday. She could choose the money box she wanted from the following three options:
Box 1 had no money in it but dad promised he would add €4 every day. Box 2 had €10 in it and a promise from dad to put €3 in every day. Box 3 had €20 in it and a promise from dad to put €2 in every day.
Which box should Sophie choose? Justify your choice with words, tables, expressions, equations or graphs.
9.1 Linear patterns in context
By the end of this section you should be able to: ● create a general formula for a linear pattern ● use an equation to solve for any term of a linear pattern
Section A Introducing concepts and building skills