Graphing buggy lab in Desmos

Goal

After reading this page, you will be able to graph data from your Buggy Lab in Desmos, and have Desmos calculate the slope and y-intercept of each data set.

Procedures

Don’t forget that Desmos does not automatically save your work; be sure to log in to your account and save your file every few minutes.

Entering data for your first buggy in Desmos

1. Copy your data from your Sheets file, other spreadsheet, or paper data table.
2. Add a folder in the first row of Desmos. Name it either Red buggy or Blue buggy (depending on which data you want to work with first).
3. In the second row on the left side, paste your data–it should appear as a table.
4. Click and hold on the circle next to the y1 table header, then make it match the color of this buggy.
5. Desmos should now look something like this:

Adding a best-fit line

1. In the Desmos row below your data table (not in the last line of the table!), type the following formula:
   • y1~mx1+b
2. Click and hold on the circle for the row you just added to make it match your buggy color.
3. Your graph should now look something like this:

Labeling your graph

1. Click the gear wrench in the upper left corner of the graph to open the options menu.
2. Add a label for your x-axis — Time (s) — and for your x-axis — Position (m).
3. We want all students to graph their data with the same scale, so set your axes as follows:
   • x-axis: -1 to 12
   • y-axis: -30 to 30
4. Your graph should now look something like this:

Adding data for your second buggy

Repeat the steps above, but this time enter data for your other buggy. Note the following before you start:

• Make sure the color of your line and data points match the color of your buggy.
• For the second set of data, the data table should have labels x2 and y2. You will need to write your new equation as:
  • y2~nx2+c
• Note that the x and y numbers are different (2 instead of 1), and in place of m and b we used n and c (since we already used m and b in the first equation).
• Your graph should now look like this:

What data you should have

• For each set of data, you should have the slope and y-intercept.
• For each set, you will also have r² and r values: These are statistical calculations; at this point you just need to know that they help you tell how close your data points match the values from the equation. The closer to 1 you get, the better the equation fits your data!

One more (optional) data analysis step

In addition to the r_² and r values, Desmos will create and plot the residuals. Residuals are calculated by finding the difference between the y-value of a row in your data table with the y-value that would come from plugging the x-value into your equation.

• Click the plot button below the residuals word (next to e₂).
• Change the color of your residuals plot so it matches your buggy color.
• Zoom in on the a-axis so you can see the residual points close up.
  • Set the y min and max to -0.1 and 0.1

Your graph should now look something like this:

The value of looking closely at the residuals is to see if they show some kind of pattern. Here are two examples:

• If they form a relatively constant curve, your equation may need to be re-written to include an exponent.
• You may also notice some data points that look way off (can you see the low red one at around y=-0.06 above?). If you get too many off the zero y-value, your r2 value will probably be not close to 1.

At this point, record any observations you have of your residuals, then re-set your graph so the y-axis range is -30 to 30.