Modeling the Flight of a Baseball


The Problem

The following table shows the distance traveled in miles,y, by a car after burning x gallons of gasoline.

x (gallons)
5
10
15
20
y (miles) 84 169 255 338

 

a). Make a scatterplot of the data. Could a linear function be used to model this data?
b). Find values a and b so that f(x) = ax + b models the distance traveled on x gallons of gasoline. Graph f and the data in the same viewing rectangle.
c). Interpret the slope of the graph of f.

a. To create a scatterplot of this data, make sure that all the Y's are clear in the menu. A quick way to turn on STAT PLOT from the menu is to press the up arrow once. Plot1 is now flasing. Press ENTER to select Plot1. This turns Plot1 on and maintains the last set of settings used. If the the settings need to be changed, follow the procedure at scatterplot.

Screen Picture of TI-83 Calculator

 

Now select and set an appropriate Viewing RectangleSince the x values range from 5 to 20, choose a range slightly larger than that, namely 0 to 25.  Since the y values range from 84 to 338, select 0 to 350.

Thus, theViewing Rectangle of  [0, 25,2] by [0, 350, 25], has been selected.  To set this Viewing Rectangle,  press WINDOWand enter 0 for Xmin, 25 for Xmax, 2 for Xscl, 0 for Ymin, 350 for Ymax,and 25 for Yscl.

Screen Picture of TI-83 Calculator


To enter the data for the scatterplot, press STAT, and select 1:Edit by pressing ENTER.  If the lists are not all cleared as shown in the screen below, go to see Clearing Lists.

 

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator


Enter the data values for X in and the data values for Y in , keeping each pair together on the same horizontal line.  Then press GRAPH.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

From the screen we see that the data appears to look linear. To be sure, we not that the x values in the table are evenly spaced. Thus we only need examine the y differences.

x
y
y-differences
5
84
 
10
169
169 - 84 = 85
15
255
255 - 169 = 86
20
338
338 - 255 = 83

Since the y differences are 85, 86, and 83, this model is approximately linear.

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