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All Tied Up In Knots
Solving a System of Equations by Graphing

Objective: To solve a system of linear equations by graphing and check the solution in a real world application.

Prior Knowledge: The student should be able to make a scatter plot of real-world data and write the equation of a trend line in point-slope form:
y = m(x – h) + k
 where m is the slope of the line, and (h, k) is a point on the line.

Materials needed:
2 unequal lengths of different size rope
meter stick
graph paper 
TI-83 graphing calculator
Group size: maximum of 3 people

Procedure:
  1. Measure the length of the thicker rope in centimeters.

  2. Tie one knot in your rope and measure its length again. Continue tying knots, measuring the length of the rope each time* and record your data in a table like the one below:

    Number of KnotsLength of Rope (in cm)
    0 
    1 
    2 
    3 
    4 
    5 

    *Have the same group member tie the knot each time to try to make it a uniform size. Before recording the length, have a group consensus of the accuracy of the measurement.

  3. Plot your points on a piece of graph paper. Make sure to put the independent variable on the x-axis, and label and number your axes appropriately.

  4. Draw a trend line on your graph (remember to get a group consensus on its location) and find the equation of the trend line. Make sure you show your work!

  5. What is the slope of your trend line? How does this slope relate to the actual rope itself?

  6. What is the y-intercept of the trend line? How does this y-intercept relate to the actual rope itself?

  7. Use your calculator to plot the points and graph the trend line to check the accuracy of your equation.

  8. Repeat steps 1 – 7 with the second length of rope. Use a separate graph for this data.

  9. Once you have both equations, graph them on the same set of axes.

  10. Find the point of intersection. Check your answer on the TI-83. If the answer isn’t the same, go back and check your work!

  11. Explain what this point tells you.

  12. How could you check to see if your explanation is correct?

  13. Show your teacher the proof of your explanation.




C Adams
C Gulliksen

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