Lecture Notes: Co-Requisite Activity 6a - Linear Equations

Introduction

• Focus on linear equations from a new perspective.
• Introduction to the story of Kai, a dog who lost weight.
• Emphasis on using real-life stories to enhance understanding of linear equations.

Kai’s Story

• Kai was an overweight dog weighing 173 pounds.
• Goal was to lose 100 pounds, set by Pam, a nurse with experience in cardiac rehab.
• Strategy: Walking, monitored diet, and gradual increase in activity.
• Progress: Initially could only walk a few steps, improved over time.
• Outcome: Success achieved through incremental steps and support from the community.

Lessons from Kai’s Story

• Start with simple steps and break big goals into smaller, manageable tasks.
• Examples of personal goals: improving health, relationships, or financial management.
• Importance of support systems (like Pam for Kai).

Application to Linear Equations

Initial Parameters

• Kai’s initial weight: 173 pounds.
• Weekly weight loss goal: 2 pounds.
• Demonstrates the concept of constant rate of change.

Tracking Weight Loss

• Creating a chart for Kai's weight over the first six weeks:
  • Week 0: 173 pounds
  • Week 1: 171 pounds
  • Week 2: 169 pounds
  • Week 3: 167 pounds
  • Week 4: 165 pounds
  • Week 5: 163 pounds
  • Week 6: 161 pounds

Graphing the Weight Loss

• Y-axis: Kai’s weight (pounds)
• X-axis: Number of weeks
• Demonstrates the concept of linear pattern and constant rate of change.

Calculating Future Weights

• Formula: New weight = Initial weight - (Rate of loss x Number of weeks)
• Example calculations:
  • 10 weeks: Weight = 153 pounds
  • 25 weeks: Weight = 123 pounds

Linear Equation

• Equation derived: W = 173 - 2T
  • W = Kai's weight
  • T = Time in weeks
• Reflects constant negative slope (weight loss)

Mathematical Concepts Explained

• Explanatory variable: Number of weeks
• Response variable: Weight
• Slope: Constant rate of change (-2 pounds/week)
• Y-intercept: Initial weight (173 pounds)

Conclusion

• Linear equations can be understood through relatable and practical examples.
• Encouragement to apply similar methodologies to personal challenges.
• Assignment: Upload notes and complete preview assignment for 6A.

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Ensure to review these notes and prepare for the next class discussion. Use the concepts learned in this lecture to solve related mathematical problems in linear equations.