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How to calculate slope & length

The slope of a line and length of a line segment can easily be calculated using only the coordinates of two points on the line.The slope of a line measures the "steepness" of the line. It represents the change in height of the line as you move forwards and backwards along the X-axis. To calculate the slope of a line you only need the coordinates of any two points on the line. The length of a line segment represents the distance between two points that lie on the line. To calculate the length of a line segment you need the coordinates of the endpoints of the segment in question.

Subtract the y-coordinate of one point on the line (point A) from the y-coordinate of a different point on the line (point B). It does not matter which points you choose for point A and point B as long as you use the same points in step 2. Record your answer for use in step 3.

Subtract the x-coordinate of point A from the x-coordinate of point B. Be sure to use the same points for point A and point B that were used in step 1. Record your answer for use in step 3.

Divide the value you obtained in step 1 by the value you caculated in step 2. This is the slope of the line shared by point A and point B.

Subtract the y-coordinate of one endpoint of the line segment (endpoint A) from the y-coordinate of the other endpoint of the line segment (endpoint B). It does not matter which endpoint you choose for endpoint A and which for endpoint B as long as you use the same points in step 2. Square the value you get and record it for use in step 3.

Subtract the x-coordinate of endpoint A from the x-coordinate of endpoint B. Be sure to use the same points for endpoint A and endpoint B that were used in step 1. Square the value you get and record it for use in step 3.

Add the squared value from step 1 to the squared value from step 2.

Take the square root of the sum found in step 3. This is the length of the line segment bounded by endpoint A and endpoint B.

Things You'll Need

  • Pencil
  • Paper
  • Calculator
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About the Author

Bryan Perkins is a writer from Baton Rouge, La. His work appears in various online publications, covering topics related to science. Perkins holds a Bachelor of Science in biological sciences from Louisiana State University.