MathIsimple
Unit 1: Linear Functions & Systems

Linear Functions & Systems

Master the fundamentals of linear functions, their properties, and systems of equations. Learn to model real-world relationships and solve complex problems using linear algebra.

4-5 Hours5 LessonsReal-world Focus

Learning Objectives

By the end of this unit, you will be able to:

1

Understand the definition of a function and use proper function notation

2

Identify and analyze linear functions in various forms

3

Calculate and interpret slope as rate of change

4

Graph linear functions and identify key features

5

Solve systems of linear equations using multiple methods

6

Apply linear functions to model real-world situations

Real-world Applications

See how linear functions are used in everyday life and professional settings.

Mobile Phone Plans

Compare different phone plans using linear functions to find the most cost-effective option based on usage.

Distance-Time Relationships

Model motion problems using linear functions to calculate speed, distance, and time relationships.

Business Optimization

Use systems of equations to optimize production, pricing, and resource allocation in business scenarios.

Unit Lessons

Five comprehensive lessons that build your understanding of linear functions step by step.

Lesson 145-60 minutes

Function Definition & Notation

Learn the fundamental concept of functions, function notation, and how to determine if a relationship is a function.

Key Skills:
Function DefinitionFunction NotationDomain & RangeVertical Line TestInput-Output Relationships
Real-world scenario: Temperature Conversion
Lesson 250-65 minutes

Linear Function Properties

Explore the general form of linear functions, slope, y-intercept, and their geometric meanings.

Key Skills:
Linear Function FormSlope CalculationY-interceptRate of ChangeGraphing Linear Functions
Real-world scenario: Mobile Phone Plans
Lesson 355-70 minutes

Slope & Rate of Change

Deep dive into slope as rate of change, calculating slope from points, and interpreting slope in real contexts.

Key Skills:
Slope FormulaRate of ChangePositive & Negative SlopeZero & Undefined SlopeReal-world Interpretation
Real-world scenario: Distance-Time Relationships
Lesson 460-75 minutes

Systems of Linear Equations

Solve systems of linear equations using substitution and elimination methods with real-world applications.

Key Skills:
Substitution MethodElimination MethodSystem SolutionsNo Solution & Infinite SolutionsProblem Solving
Real-world scenario: Business Optimization
Lesson 565-80 minutes

Linear Function Applications

Apply linear functions to solve complex real-world problems including optimization and modeling scenarios.

Key Skills:
Problem ModelingFunction CreationOptimizationBreak-even AnalysisPredictive Modeling
Real-world scenario: Cost-Benefit Analysis

Ready to Start Learning?

Begin with function definitions and build your way up to solving complex systems of equations.