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 Group size:
TI-83 graphing calculator
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)|
*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.