Slope Calculation

Understanding Slope Calculation

• Definition of Slope:

  • The slope of a line is a measure of its steepness, typically defined as the change in the y-coordinates (rise) divided by the change in the x-coordinates (run) between two points on the line.
  • Formula for calculating the slope (m):
    $m = \frac{y<em>2 - y</em>1}{x<em>2 - x</em>1}$

• Given Points:

  • The two points provided are:
  • Point 1: (5, 1)
  • Point 2: (8, 4)

• Identifying Coordinates:

  • From Point 1, the coordinates are:
  • $(x<em>1, y</em>1) = (5, 1)$
  • From Point 2, the coordinates are:
  • $(x<em>2, y</em>2) = (8, 4)$

• Calculating the Slope:

  1. Determine the Change in y (rise):
  • $y<em>2 - y</em>1 = 4 - 1 = 3$
  1. Determine the Change in x (run):
  • $x<em>2 - x</em>1 = 8 - 5 = 3$
  1. Substitute into the formula:
  • $m = \frac{3}{3} = 1$

• Conclusion about Slope:

  • The slope of the line containing the points (5, 1) and (8, 4) is 1, which indicates that for every unit the line moves in the x-direction, it moves one unit in the y-direction as well.