Education Technology

Investigating Properties of Lines in the Plane

Published on 06/09/2008

Activity Overview

In this activity, students draw a line and determine its slope. They understand that the slope of a line is actually the ratio of rise over run.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print page 47 from the attached PDF file for your class
  • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Display the axes and draw a line from the third quadrant to the first quadrant, passing through the origin
  • Construct two points on the line in quadrant I, and label them A and C
  • Construct a line parallel to the x-axis through A and a line parallel to the y-axis through C
  • Label the point of intersection of the lines as B
  • Construct and measure segments AB and BC, and compute the ratio (BC)/(AB)
  • Understand that this ratio of change in y-coordinate to change in x-coordinate is called the slope of the line
  • Move A and C along the line and observe that the slope of a line remains constant at all points
  • Determine the equation of the line, and observe that as the line is rotated around the origin, the slope of the line is equal to the coefficient of x in the equation
  • Understand that the y-coordinate of a point on a line is the product of the x-coordinate and the slope
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary