Slope of a Line Calculation

Finding the Slope of a Line

Key Concepts

  • Slope Definition: The slope of a line is a measure of its steepness and is calculated as the ratio of the change in y-values to the change in x-values between two points on the line. It is often denoted by the letter m.

Slope Formula

  • Slope Formula: If we have two points \((x1, y1)) and \((x2, y2)\), the slope ( m ) is given by the formula:
    m=y<em>2−y</em>1x<em>2−x</em>1m = \frac{y<em>2 - y</em>1}{x<em>2 - x</em>1}

Example Calculation

  1. Identify Points: Given the points (3,5) and (-8,5):

    • Point 1: ((x1, y1) = (3, 5))
    • Point 2: ((x2, y2) = (-8, 5))

  2. Substitute Values into the Slope Formula:

    • Calculate (y2 - y1):
      y<em>2−y</em>1=5−5=0y<em>2 - y</em>1 = 5 - 5 = 0
    • Calculate (x2 - x1):
      x<em>2−x</em>1=−8−3=−11x<em>2 - x</em>1 = -8 - 3 = -11
    • Therefore, the slope is calculated as follows:
      m=0−11m = \frac{0}{-11}

  3. Evaluate the Slope:

    • Since the numerator is 0, we conclude:
      m=0m = 0

Conclusion

  • Final Answer: The slope of the line is 0, indicating that the line is horizontal.
  • Multiple Choice Options:
    • OA. The slope of the line is 0.
    • OB. The slope is undefined. (Not applicable in this case as the slope is clearly defined.)