Question

the table shows the percentage of male and female populations in a certain county employed in the work force in certain years since 1989. model the data algebraically with linear equations of the form ( y = mx + b ). use the 1989 and 1995 data to complete the slopes. use the year as ( x ) and the employment data as ( y ).

the equation that represents womens employment statistics is ( y=square ).
(use integers or decimals for any numbers in the expression. round to the nearest hundredth as needed.)

the equation that represents mens employment statistics is ( y=square ).
(use integers or decimals for any numbers in the expression. round to the nearest hundredth as needed.)

Explanation:

Step1: Calculate the slope for women

For women, in 1989 ($x_1 = 0$, $y_1=30.2$) and 1995 ($x_2 = 6$, $y_2 = 57.3$).
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
So, $m_w=\frac{57.3 - 30.2}{6-0}=\frac{27.1}{6}\approx4.52$.
Using the point - slope form $y - y_1=m(x - x_1)$, with $(x_1,y_1)=(0,30.2)$ and $m = 4.52$, the equation is $y=4.52x + 30.2$.

Step2: Calculate the slope for men

For men, in 1989 ($x_1 = 0$, $y_1 = 91.3$) and 1995 ($x_2=6$, $y_2 = 64.2$).
Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_m=\frac{64.2-91.3}{6 - 0}=\frac{- 27.1}{6}\approx - 4.52$.
Using the point - slope form $y - y_1=m(x - x_1)$, with $(x_1,y_1)=(0,91.3)$ and $m=-4.52$, the equation is $y=-4.52x + 91.3$.

Answer:

The equation that represents women's employment statistics is $y = 4.52x+30.2$.
The equation that represents men's employment statistics is $y=-4.52x + 91.3$.