The number of men in the work force in millions from 18990

The number of men in the work force ( in millions) from 18990 to 1990 can be approximated by the line connectring these points (18890, 18.1) (1990, 69.5)

A. write the equation of this line

B. inerpret the slope of this line

Solution

There appears to be a mistake in the data given. The first year should probably be 1890 and not 18990. If not, the appropriate changes may be made, or a comment can be made so that the answer may be amended.

Let the equation of the required line be y = mx + c, where m is its slope and c is the y- intercept. Since the line passes through the points (1890, 18.1) and (1990, 69.5), therefore, m = (69.5-18.1)/( 1990-1890) = 51.4/100 = 514/1000. Then the equation of the line chages to y = (514/ 1000) x +c .Further, since the line passes through the poinr (1990,69.5), on substituting x = 1990 and y = 69.5 in this equation, we get 69.5 = (514 / 1000) * 1990 + c or, 69.5 = 1022.86 +c so that c = 69.5-1022.86 = -953.36 . Hence the equation of the required line is y = 0.514x - 953.36.

The slope of the line represents the rate of change of the number of men (in millions) between 1890 and 1990.