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Student Page 3.6.2 Linear Sovereignty

Play Linear Sovereignty until each player has had 3 turns. Use the gameboard in Figure  39 

Linear Sovereignty Rules.

On your turn:

  1. Draw a line that goes through two or more points on the gameboard. All lines must be functions. (What types of lines does this rule eliminate?)

  2. State a correct equation for the line you drew.

  3. Scoring is as follows. You must justify your score.

    • 1 point for each point on the gameboard that is on the line.

    • 1 point for algebraically determining the intersection point of your line with another line. The intersection point cannot be a point already on the gameboard.

    • 1 point for constructing a line parallel or perpendicular to an existing line.

  4. If an error is made in finding or justifying an equation or point of intersection, the player correcting the error steals the point(s).

  5. Play moves to the left. The game ends when each player has had three turns.

To Win.

The player with the most points at the end of the game wins.

Answer the following questions when you have finished playing Linear Sovereignty:


How did you determine that two lines were parallel?


Were you able to determine that two lines were perpendicular? How?


How can you determine the coordinates of a point of intersection?


Look at the graph again. How many pairs of parallel lines are possible?


How many pairs of perpendicular lines are possible?

Figure Linear Sovereignty Gameboard