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:- Measure the length of the thicker rope in centimeters.
- 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 Knots | Length 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.
- 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.
- 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!
- What is the slope of your trend line? How does this slope relate to the actual rope itself?
- What is the y-intercept of the trend line? How does this y-intercept relate to the actual rope itself?
- Use your calculator to plot the points and graph the trend line to check the accuracy of your equation.
- Repeat steps 1 – 7 with the second length of rope. Use a separate graph for this data.
- Once you have both equations, graph them on the same set of axes.
- 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!
- Explain what this point tells you.
- How could you check to see if your explanation is correct?
- Show your teacher the proof of your explanation.