SITE-A teams: Lesson 6

 

In 1970, 130 African-American women held elected Federal Offices in the United States. By 1990, the number had increased to 1950. In 1973, Barbara Jordan became the first African-American woman from a Southern state to serve in the United States Congress.

 

Can you find the average rate of change in the number of African-American women holding elected Federal Offices in the United States?

If we let x be the year and y be the number of African-American women holding elected Federal Offices in the United States, then we have two data point -- (1970, 130) and (1990, 1950). Two points determine a line and the slope of that line is the average rate of change.

Turn on the CASIO fx7400G.

Ac_on.gif (1767 bytes)

Use your cursor arrows to highlight the STAT menu and press exe.gif (1747 bytes) or just press 2.gif (1709 bytes) when at the main menu screen.

 

Use your cursor arrows to move to the first cell in List1 and enter the years. After entering each year make sure to press exe.gif (1747 bytes) to go down to the next cell.

 

Use your cursor arrows to move to the first cell in List2 and enter the number of African-American women holding elected Federal Offices in the United States for the respective year. After entering an amount make sure to press exe.gif (1747 bytes) to go down to the next cell.

Press f2.gif (1726 bytes) (CALC)

Press f4.gif (1732 bytes) (SET)

Scroll down and set the parameters as follows:

2Var X :                     List1         Press f1.gif (1719 bytes) if necessary.

2Var Y :                     List2         Press f2.gif (1726 bytes) if necessary.

2Var F :                          1         Press f1.gif (1719 bytes) if necessary.

Press quit.gif (1764 bytes)

Press f2.gif (1726 bytes) (CALC)

Press f3.gif (1726 bytes) (REG)

Press f1.gif (1719 bytes) ( X )

What appears is:

LinearReg

a = 91

b = - 1.791+05

r = 1

y = a x + b

The average rate of change is 91 per year, the slope of the equation. In addition, we also have the equation of the line that passes through the two data points, that is y = 91 x - 1.791 x 105

 

Press quit.gif (1764 bytes)

Press menu.gif (1772 bytes)

Turn off the CASIO fx7400G.

shiftac.gif (1924 bytes)(OFF)

 

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Side Note -- This use of technology replace the struggle that teachers have with students who must memorize the following formulas correctly so that they can use them to solve problems such as the one above:

Given two points ( x1, y1 ) and ( x2, y2 ), the slope can be obtained by either of the following formulas:

formauls4.gif (2150 bytes)

The equation of the line through those points is then obtained by using the formula

y - y1 = m ( x - x1 )

or

y - y2 = m ( x - x2 )

The confusion of students mixing x1 with y2 or x2 with y1 is well know among those of us that have taught algebra.