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

A9.4 – Graphing Functions

  • 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