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.
year 1989 1990 1991 1992 1993 1994 1995
women (%) 30.8 35.1 40.4 44.6 49.1 52.6 57.3
men (%) 93.9 89.6 84.3 80.1 75.6 72.1 67.4
the equation that represents womens employment statistics is y = 4.42x + 30.8 (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 = (use integers or decimals for any numbers in the expression. round to the nearest hundredth as needed.)

Explanation:

Step1: Identify two - point data for men

For men, in 1989 ($x_1 = 1989$, $y_1=93.9$) and 1995 ($x_2 = 1995$, $y_2 = 67.4$).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{67.4 - 93.9}{1995 - 1989}=\frac{- 26.5}{6}\approx - 4.42$.

Step3: Find the y - intercept $b$

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(1989,93.9)$ and $m=-4.42$. Then $y-93.9=-4.42(x - 1989)$. Expand to get $y-93.9=-4.42x+4.42\times1989$. So $y=-4.42x+4.42\times1989 + 93.9$. Calculate $4.42\times1989+93.9=4.42\times1989+93.9=8791.38+93.9 = 8885.28$. The equation of the line is $y=-4.42x + 8885.28$. But we can also use the general form $y=mx + b$ and substitute $m=-4.42$ and the point $(1989,93.9)$ into $y = mx + b$ to solve for $b$: $93.9=-4.42\times1989+b$. Then $b=93.9 + 4.42\times1989=93.9+8791.38 = 8885.28$.

Answer:

$y=-4.42x + 8885.28$