Concept of Slope

The following construction shows a line that runs through the origin of the coordinate system and a moveable point M.
On the left, you can also see the corresponding linear equation.

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  1. Drag point M to the positions (4, 6), (6, 0), (2, -3) and (0, -2). Describe the location of the line relative to the coordinate axes for every position of M.
  2. Describe how to draw the red triangle.
    Hint: Use the coordinate axes as well as the origin and point M.
  3. Look at the equation of the line. How is the equation connected to the triangle?
  4. Try to write the equation of this line in a more general form. Use the name “rise” for the vertical and “run” for the horizontal side of the triangle.

Judith Preiner, December 20, 2006, Created with GeoGebra Updated by S.H. Lapinski

Please direct questions and comments to HCPS Mathematics Specialist Henrico County Public Schools, 2009