Key Concepts of Horizontal and Vertical Lines

Introduction

• Discussion of horizontal (yellow) and vertical (blue) lines.
• Importance of understanding their key features, particularly the slope.

Understanding Slope

• Slope Definition: Slope (denoted by M) = Rise / Run
  • "Rise" refers to how much a line goes up or down.
  • "Run" refers to how much a line moves left or right.

Horizontal Lines

• Slope of Horizontal Line:
  • Rise = 0 (no vertical movement).
  • Run = any non-zero number.
  • Slope (M) = 0/Run = 0.
  • Conclusion: The slope of a horizontal line is always 0.

Vertical Lines

• Slope of Vertical Line:
  • Rise = some number (vertical movement).
  • Run = 0 (no horizontal movement).
  • Slope = Rise/0 (undefined, division by zero).
  • Conclusion: The slope of a vertical line is always undefined.

Example Problems

Graphing Equations

• Equation: y = -4

  • Horizontal line at y = -4.
  • All points on this line have the same y-value of -4.

• Equation: x = 3

  • Vertical line at x = 3.
  • All points on this line have the same x-value of 3.

Determining Slope

• Example with Horizontal Line

  • Given: A line where x = -2.
  • Selected points show rise = 0, run = 2.
  • Slope = 0/2 = 0.

• Example with Vertical Line

  • Given: A point (-5, -2).
  • Vertical line passing through this point.
  • All points have the same x-value of -5.
  • Equation: x = -5.

Final Example

• Equation of a Line
  • All points have the same x-value of -9.
  • Equation: x = -9.

Conclusion

• Understanding horizontal and vertical lines is crucial in analyzing their slopes.
• Remember: Horizontal lines have a slope of 0, while vertical lines have an undefined slope.