## Module-Lessons

VII. - Equations and Inequalities of Two Variables and Functions # Modules

Algebra7 – Solving Linear Equations and Inequalities of Two Variables

A7.1 – Defining Linear Equations of Two Variables and Their Solutions

• Solutions of a Linear Equation
• Cartesian Coordinate System
• Plotting Points
• Graph of the Solutions of a Linear Equation
• Showing All Solutions of a Linear Equation
• Special Case-Horizontal Lines
• Special Case-Vertical Lines
• Conclusion

A7.2 – Graphing Linear Equations of Two Variables

• Graphing Linear Equations Using Tables
• Graphing Linear Equations Using Intercepts
• Graphing Linear Equations Slope-Intercept
• Negative Slope
• Positive Slope
• Conclusion

A7.3 – Graphing Linear Inequalities of Two Variables

• Graphing an Inequality with One Variable on a Number Line
• Graphing an Inequality with Two Variables on a Coordinate Plane
• Boundary Line
• Test Point
• Conclusion

A7.4 – Solving Consumer/Business Problems Using Linear Equations and Inequalities of Two Variables

• Concession Stand Application Problem
• Football Tickets Application Problem
• DJ Service Application Problem
• Conclusion

Algebra8 – Writing Linear Equations of Two Variables

A8.1 – Finding Slope

• Slope of a Line
• Comparing Slopes of Lines
• Negative Slopes
• Opposite Slopes
• Discovering the Slope Formula
• Slope Formula
• Horizontal Lines
• Vertical Lines
• Parallel Lines
• Perpendicular Lines
• Conclusion

A8.2 – Writing Equations of Lines, Given the Slope and y-Intercept

• Equations and Lines
• Slope-Intercept Form
• Graphs and Slope-Intercept Form
• Determining Slope and y-intercept
• Writing Equations
• Parallel and Perpendicular Lines
• Reciprocals
• Conclusion

A8.3 – Writing Equations of Lines, Given a Point and the Slope or Two Points

• Defining Point-Slope Form
• Using Point-Slope Form
• Application Problem
• Parallel and Perpendicular Lines
• Finding the Equation
• Conclusion

A8.4 – Solving Linear Equations in Two Variables When Parameters Are Changed

• Parameters
• Using Parameters to Determine an Equation
• Changing the Parameters m and b
• Perpendicular Lines
• Linear Equations
• Converting from Standard Form to Slope-intercept Form
• Conclusion

Algebra9 – Using Functions

A9.1 – Defining Relations and Functions

• Introduction to Function Machine
• Relations
• Domain and Range of a Relation
• Mapping Diagram
• Table
• Graph of a Relation
• Set-Builder Notation
• Ways to Represent a Relation
• Function
• Constant Function
• Linear Function
• Vertical Line Test
• Nonlinear Function
• Function Machine
• Conclusion

A9.2 – Evaluating Functions

• Functions
• Domain and Range
• Function Notation
• Evaluating a Function
• Functions on the Coordinate Plane
• Conclusion

A9.3 – Writing Functions from Patterns

• Input-Output Table
• Writing a Function from a Pattern
• Application Problem – Job
• Scatterplot
• Slope
• Function Mapping and Scatter Plots
• Conclusion

• Definition of Linear Function
• Graphing the Linear Function
• Graphing the Constant Function
• Absolute Value Function
• Translating Parent Graph
• Graphing Piecewise Functions
• Conclusion

A9.5 – Solving Problems Using Functions

• Real-World Application
• Formulas as Functions
• Real World Application #2
• Mowing Service
• Pizza Sharing Function
• Health-Related Function
• Conclusion

A9.6 – Evaluating Composite Functions

• Sale Price Function
• Defining Composition of Two Functions
• Evaluating
• Example
• Real-World Application – Finding the Original Price
• Determining Inverses
• Conclusion

Algebra10 – Solving Systems of Linear Equations and Inequalities

A10.1 – Solving Systems of Linear Equations by Graphing

• System of Linear Equations
• Determine Whether an Ordered Pair is a Solution
• Solving Systems of Linear Equations by Graphing
• Consistent, Inconsistent, Dependent, or Independent
• Conclusion

A10.2 – Solving Systems of Linear Equations by Elimination

• Solutions to a System of Equations
• Elimination by Addition of a System
• Elimination by Multiplication of One Equation in a System
• Elimination by Multiplication of Both Equations
• Overview of Elimination Method
• System With No Solution
• System With Infinitely Many Solutions
• Conclusion

A10.3 – Solving Systems of Linear Equations by Substitution

• Methods of Solving Systems of Linear Equations
• Solving of System of Linear Equations Using the Substitution Method
• Checking a Solution to a System of Linear Equations
• Solving a System of Linear Equations of Two Variables
• Solving a System of Linear Equations with Infinitely Many Solutions by Substitution
• Systems of Linear Inequalities Whose Graphs Have Parallel Boundaries
• Conclusion

A10.4 – Solving Systems of Linear Inequalities by Graphing

• Solving Linear Inequalities of Two Variables
• Graphing a System of Linear Equations of Two Variables
• Systems of Linear Inequalities Whose Graphs Have Horizontal and Vertical Boundaries
• Graphing a System of Three Linear Inequalities
• Systems of Linear Inequalities Whose Graphs Have Parallel Boundaries
• Conclusion

A10.5 – Solving Problems Using Systems of Linear Equations and Inequalities

• Money Saving Problem – No Interest
• Problem – Solving Tips
• Money Saving Problem with Interest
• Rate/Time/Distance Problem
• Polygon Dimension Problem
• Mixture Problem
• Hours Worked/Salary Inequality Problem
• Conclusion