Lecture on Converting Equations to Slope-Intercept Form and Graphing

Key Concepts

1. Standard Form of an Equation: The equation is given as ax + by = c.
2. Slope-Intercept Form: The goal is to convert the equation to the form y = mx + b, where:
   • m is the slope
   • b is the y-intercept

Steps to Convert to Slope-Intercept Form

1. Move x term to the right side of the equation.
   • For example, from 2x + y = 3, move 2x to the right to get y = -2x + 3.
2. Solve for y: Ensure y is by itself on one side of the equation.

Example 1

• Given: 2x + y = 3
• Convert to Slope-Intercept Form:
  • Move 2x to the right: y = -2x + 3
• **Identify Slope and Y-Intercept: **
  • Slope m = -2
  • Y-intercept b = 3
• Graphing:
  • Plot y-intercept (0, 3)
  • Use slope m = -2 (rise/run): Move down 2 units and 1 unit to the right.
  • Plot additional points and draw the line.

Example 2

• Given: 3x - 4y = 12
• Convert to Slope-Intercept Form:
  • Move 3x to the right: -4y = -3x + 12
  • Divide every term by -4
    • y = 3/4x - 3
• Identify Slope and Y-Intercept:
  • Slope m = 3/4
  • Y-intercept b = -3
• Graphing:
  • Plot y-intercept (0, -3)
  • Use slope m = 3/4 (rise/run): Move up 3 units and 4 units to the right.
  • Plot additional points and draw the line.

General Tips for Graphing

1. Plot the y-intercept first: This is where the line crosses the y-axis.
2. Use the slope to find additional points: Slope = rise/run (move up/down and right).
3. Extend the graph if necessary: If more points are needed for accuracy.