Question

find linear models for each set of data. in what year will the two quantities be equal?
life expectancy at birth (1970 - 2000)

year	1970	1975	1980	1985	1990	1995	2000
women (years)	76.1	77.8	78.6	79.5	79.9	80.3	81.1

let x be the number of years since 1970. what is the linear model for men?
y = □x+□
(round to three decimal places as needed.)

Explanation:

Step1: Find the slope for men

The slope $m$ of a line $y = mx + b$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,67.1)$ (corresponding to year 1970 where $x = 0$ and life - expectancy for men $y = 67.1$) and $(x_2,y_2)=(5,68.9)$ (corresponding to year 1975 where $x = 5$ and life - expectancy for men $y = 68.9$). Then $m=\frac{68.9 - 67.1}{5-0}=\frac{1.8}{5}=0.360$.

Step2: Find the y - intercept for men

The y - intercept $b$ is the value of $y$ when $x = 0$. When $x = 0$ (year 1970), for men, $y=67.1$. So $b = 67.100$.

Answer:

$y = 0.360x+67.100$