Graphing Horizontal or Vertical Lines

Introduction

• Purpose: Learn to graph horizontal and vertical lines.
• Context: Part of "Thinking Mathematically" series.

Horizontal Lines

• Definition: A horizontal line has a slope of 0, denoted as ( m = 0 ).
• Equation Form: ( y = mx + b ) simplifies to ( y = b ), where ( b ) is the y-intercept.
• **All horizontal lines have equations of the form y = b.
• Graphing Example:
  • Equation: ( y = -4 )
  • Order Pairs:
    • (( -2, -4 ))
    • (( 0, -4 ))
    • (( 3, -4 ))
  • Interpretation: All y-values are -4; x-values can vary. Think of y = -4 as 0x + 1y = -4.
  • Graph: Plot the points and draw a line through them to form a horizontal line.**

Vertical Lines

• Definition: A vertical line has undefined slope; x-value is constant.
• Equation Form: ( x = a ), where ( a ) is a constant.
• Graphing Example:
  • Equation: ( x = -2 )
  • Order Pairs:
    • (( -2, -3 ))
    • (( -2, 0 ))
    • (( -2, 2 ))
  • Interpretation: All x-values are -2; y-values can vary. Think of 1x + 0y = -2.
  • Graph: Plot the points and draw a line through them to form a vertical line.

Summary

• Horizontal lines are characterized by constant y-values and are graphed using the equation ( y = b ).
• Vertical lines are characterized by constant x-values and are graphed using the equation ( x = a ).
• Graphing involves plotting points and drawing lines through them to visually represent the equations.