Algorithms

Materials needed: graph paper, pencil, ruler

1. Follow the list of instructions below:

i. Draw a Cartesian plane on your graph paper

ii. Carefully graph the following system of equations:

y = 2x - 4

y = -x +2

iii. Choose a point on one of the lines, and mark it with your pencil.

iv. Draw a vertical line through the marked point, and mark the plac where it crosses the

other line.

v. Through this new point, draw a horizontal line (a line through this point and parallel with

the x axis) and mark the place where it crosses the other line in the system.

vi. Mark this new point.

vii. Repeat steps iv, v, and vi until you converge on a single point.

2. To what special point do you converge?

3. Try the set of directions with another system of linear equations. Do you converge on a special

point this time?

4. Fill in the blank in the title of this algorithm.

5. There is a "loop" in this algorithm. Where is it?

6. Why is it called a "loop"?

7. Will the algorithm always work? Why or Why not?