Math Antics: Calculating Slope and Distance

Introduction

• The video covers linear functions on a 2D coordinate plane.
• Focus on two new equations for calculating the slope of a line and the distance between two points on a line.

Definitions and Concepts

• Linear Function: Represented by y = mx + b.
• Slope (m): Slope = (delta Y) over (delta X), which is the change in Y divided by the change in X. Sometimes referred to as "rise over run."
• Distance Formula: Distance = square root of [(delta X) squared + (delta Y) squared], derived from the Pythagorean Theorem.

Fundamental Steps

1. Identify Two Points: Name them "Point 1" (X1, Y1) and "Point 2" (X2, Y2) on the coordinate plane.
2. Create a Right Triangle:
   • Draw vertical and horizontal lines from each point to form a triangle.
   • Label sides as "change in X" (delta X) and "change in Y" (delta Y).

Equations

• Delta Calculations:
  • Delta X = X2 − X1
  • Delta Y = Y2 − Y1
• Slope Equation: Slope = (delta Y) / (delta X)
• Distance Formula: Distance = √[(delta X)² + (delta Y)²]

Worked Examples

1. Example 1:

   • Given Points: (X1, Y1) = (-2, 0), (X2, Y2) = (4, 3).
   • Delta X = 6, Delta Y = 3.
   • Slope = 0.5
   • Distance = √45 or 6.708 (rounded).

2. Example 2:

   • Given Points: (X1, Y1) = (-3, 5), (X2, Y2) = (1, -2).
   • Delta X = 4, Delta Y = -7.
   • Slope = -1.75
   • Distance = √65 or 8.062 (rounded).

Additional Points

• Pythagorean Theorem: Used for the distance formula.
• Significance of Delta Values:
  • Delta signs indicate direction and are crucial for finding the correct slope.
  • Lengths are the absolute values of deltas.

Conclusion

• Practice calculating slope and distance with various points for proficiency.
• Visit mathantics.com for more resources.