**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.