3.4   Graphs, Models, and Slope
Homework 3,5,7,8,15,23,27, All Odd 31-53

A.  ScatterPlots.
Ex.  Disease Rate. The following table lists the number of cases of chicken pox in the United States for various years (Source: Centers for Disease Control and Prevention).  Let List 1 values be the number of years since 1980 and let List 2 values be the number of cases of chicken pox.  Use the data to draw a line graph.

YEAR

LIST 1 (Number of years since 1980).

LIST 2 (Number of cases of chicken pox).

1980

0

190,894

1990

10

173,099

1991

11

147,076

1992

12

158,364

1993

13

134,722

1994

14

151,219

1995

15

120,624

Use the calculator to form a scatterplot, by entering given values into Lists 1 and 2, as follows. Go to STAT, select 1:Edit. Clear lists if needed by going with the up-arrow to the name of each list, hit CLEAR, then the down-arrow. Enter the values as shown.


Go to the Y= window to be sure that you have no equations entered into this window. Using the up-arrow, move up to Plot 1, push ENTER, use down-arrow to move back down, and Plot 1 should now be highlighted. Push ZOOM, 9 to get the scatterplot as shown below.

 



To draw a line graph through these plotted points, push 2nd STATPLOT, select 1, on second line for Type:, choose the line icon by moving to it and pushing ENTER. Push ZOOM 9 again to get the line graph as shown.




Practice Problem:
P. 173, #4

B.  Using an equation to describe a problem-situation.

Ex.  Value of Computer Software. The value v of a shopkeeper’s inventory software program, in hundreds of dollars, is given by , where t is the number of years since the shopkeeper first bought the program. Graph the equation and use the graph to estimate what the program is worth 4 years after it was purchased.

 

Enter this equation into the calculator in the y= window


(Notice that Plot 1 has been un-highlighted, so as to be able to graph the equation. This was done by moving up to Plot 1, pushing ENTER, then moving down.)

Since x (representing time) cannot be a negative number, let’s change the graphing window, as follows.


GRAPH



Use the graph or the table to answer the question.



We see that after 4 years after first purchased, the program is worth $300.

Practice Problem:

p. 174, # 14


C.  Rate

Rate of change is the amount of change per one unit of time.
Ex.  If defense outlays changes from $292 million in 1993 to $282 million in 1994 to $272 million in 1995, we can determine the rate of change to be $100 million per year.

Practice Problem:

p.175, # 28


D.  Slope

The slope of a line is constant. Slope is a ratio (fraction) of the vertical change divided by the horizontal change between any two points on the line.

.

Given any two points on a line, we can calculate the slope of the line using this ratio as follows in the given example.

 

Ex.  Find the slope of the line going through the points (4, -2) and (3, 7).

 

 

Enter the values into the slope ratio.

 

Practice Problem:

p. 176, # 40

 


Final note: Grade of a road is simply slope expressed as a percent.