Chapter 1.1, Problem 15E

Solution

To find: The slope intercept form of line for the males and females.

The slope intercept form of line for males is $y=-0.254x+83.4$ and slope intercept form of line for females is $y=0.418x+37.7$ .

Given:

The data of labor force in the form of table is

Year	Female	Male
1960	37.7	83.4
1965	39.3	80.5
1970	43.3	79.6
1975	46.3	77.2
1980	51.5	77
1985	54.5	76.1
1990	57.5	76.3
1995	58.9	74.6
2000	59.9	74.7
2005	59.3	73.2
2010	58.6	70.7

The $x$ coordinate should be $x_1=0$ , $x_2=50$ , $y$ coordinate for males and females should be according to the values ,slope intercept form of the line is of the form $y=mx+b$ .

Formula used:

  $m=\frac{y_2-y_1}{x_2-x_1}$.

Calculation:

Calculation of slope intercepts form of line for males.

Taking $x=0$ , $x_2=50$ and $y_1=83.4$ , $y_2=70.7$

Substitute the values in the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

  $\begin{array}{c}m=\frac{70.7-83.4}{50-0}\\ =-0.254\end{array}$

Substitute the value of $m$ , $x_1$ , $y_1$ in the equation $y_1=m{x}_1+b$ .

  $\begin{array}{c}83.4=\left(-0.254\right)\times 0+b\\ b=83.4\end{array}$

Substitute the values of $m$ and $b$ in the formula $y=mx+b$ .

  $y=-0.254x+83.4$ .

Calculation of slope intercepts form of line for females.

Taking $x=0$ , $x_2=50$ and $y_1=37.7$ , $y_2=58.6$

Substitute the values in the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

  $\begin{array}{c}m=\frac{58.6-37.7}{50-0}\\ =0.418\end{array}$

Substitute the value of $m$ , $x_1$ , $y_1$ in the equation $y_1=m{x}_1+b$ .

  $\begin{array}{c}37.7=\left(0.418\right)\times 0+b\\ b=37.7\end{array}$

Substitute the values of $m$ and $b$ in the formula $y=mx+b$ .

  $y=0.418x+37.7$ .