Lecture on Converting Equations to Slope-Intercept Form

Introduction

• Discuss converting equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b).
• Importance of identifying the slope (m) and y-intercept (b) for graphing.

Example 1: Convert 2x + y = 3 to Slope-Intercept Form

• Standard Form: 2x + y = 3
• Objective: Convert to y = mx + b

Steps to Convert:

1. Solve for y:
   • Move 2x to the right side: y = -2x + 3
   • Equation in slope-intercept form: y = -2x + 3

Identify Slope and Y-Intercept:

• Slope (m): -2
• Y-Intercept (b): 3

Graphing the Equation:

1. Plot the Y-Intercept:
   • Point (0, 3) on the graph.
2. Use the Slope (-2):
   • Slope as rise over run: Rise -2, Run 1
   • From (0, 3), go down 2 units and 1 unit right to (1, 1)
3. Draw the Line:
   • Connect the points to form a line.

Example 2: Convert 3x - 4y = 12 to Slope-Intercept Form

• Standard Form: 3x - 4y = 12
• Objective: Convert to y = mx + b

Steps to Convert:

1. Move 3x to the Right Side:
   • -4y = -3x + 12
2. Divide Every Term by -4:
   • y = (3/4)x - 3

Identify Slope and Y-Intercept:

• Slope (m): 3/4
• Y-Intercept (b): -3

Graphing the Equation:

1. Plot the Y-Intercept:
   • Point (0, -3) on the graph.
2. Use the Slope (3/4):
   • Rise 3, Run 4
   • From (0, -3), go up 3 units and 4 units right to (4, 0)
3. Draw the Line:
   • Connect the points to form a line.

Key Takeaways

• Converting equations to slope-intercept form allows for easy identification of slope and y-intercept.
• The slope (m) helps in determining the rise and run for plotting additional points.
• Start with plotting the y-intercept and use the slope to find subsequent points for graphing.