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
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Example 1:
- Equation: \(y = 2x + 1\)
- Steps to graph:
- Identify slope and y-intercept.
- Create a table of values.
- Draw the line.
- Include a graph.
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Example 2:
- Equation: \(y = -\frac{1}{2}x + 3\)
- Steps to graph:
- Identify slope and y-intercept.
- Create a table of values.
- Draw the line.
- Include a graph.
4. Graphing Inequalities
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Example 1:
- Inequality: \(y < 2x + 3\)
- Steps to graph:
- Graph the boundary line \(y = 2x + 3\) with a dashed line.
- Shade the area below the line.
- Include a graph.
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Example 2:
- Inequality: \(y \geq -\frac{1}{3}x + 1\)
- Steps to graph:
- Graph the boundary line \(y = -\frac{1}{3}x + 1\) with a solid line.
- 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.
- Solve the system:
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.