02052 Algebra 1 A - 2-Variable Equations & Inequalities Portfolio

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Creating a portfolio for a unit on 2-variable equations and inequalities in Algebra 1 is a great way to organize your understanding and showcase your learning. Below is an outline that can help you structure your portfolio effectively:

Algebra 1 Portfolio: 2-Variable Equations & Inequalities


1. Introduction

  • Objective: Describe what you learned about 2-variable equations and inequalities.
  • Importance: Explain why understanding these concepts is crucial in algebra and real-life applications.

2. Key Concepts

  • Definition of 2-Variable Equations: Explain what a 2-variable equation is (e.g., \(y = mx + b\)).
  • Types of 2-Variable Equations:
    • Linear Equations
    • Non-linear Equations (such as quadratic)
  • Definition of Inequalities: Describe 2-variable inequalities (e.g., \(y > mx + b\)).
  • Graphing: The importance of graphing solutions.

3. Graphing 2-Variable Equations

  • Example 1:

    • Equation: \(y = 2x + 1\)
    • Steps to graph:
      1. Identify slope and y-intercept.
      2. Create a table of values.
      3. Draw the line.
    • Include a graph.
  • Example 2:

    • Equation: \(y = -\frac{1}{2}x + 3\)
    • Steps to graph:
      1. Identify slope and y-intercept.
      2. Create a table of values.
      3. Draw the line.
    • Include a graph.

4. Graphing Inequalities

  • Example 1:

    • Inequality: \(y < 2x + 3\)
    • Steps to graph:
      1. Graph the boundary line \(y = 2x + 3\) with a dashed line.
      2. Shade the area below the line.
    • Include a graph.
  • Example 2:

    • Inequality: \(y \geq -\frac{1}{3}x + 1\)
    • Steps to graph:
      1. Graph the boundary line \(y = -\frac{1}{3}x + 1\) with a solid line.
      2. Shade the area above the line.
    • Include a graph.

5. Solutions to Systems of Equations

  • Methods of Solving:
    • Graphing
    • Substitution
    • Elimination
  • Example of a System:
    • Solve the system:
      • \(y = 2x + 1\)
      • \(y = -x + 4\)
    • Show the solution via graph and algebraic methods.

6. Applications of 2-Variable Equations and Inequalities

  • Real-world scenarios (e.g., budgeting, planning, etc.).
  • Example problem: If you have $100 to spend on two types of tickets (to a concert and a football game), write and graph the inequality representing your budget.

7. Reflection

  • What did you find most challenging?
  • What did you enjoy the most about the unit?
  • How will you use these skills in the future?

8. Additional Resources

  • List of helpful websites, videos, or textbooks to further understand 2-variable equations and inequalities.

This outline allows you to showcase your understanding of 2-variable equations and inequalities through various examples, graphical representation, applications, and personal reflections. Make sure to include diagrams, charts, and any relevant calculations to enhance your portfolio visually and effectively.