find linear models for each set of data. in what year will the two quantities be equal?\nlife expectancy at…

find linear models for each set of data. in what year will the two quantities be equal?\nlife expectancy at birth (1970 - 2000)\n| year | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 |\n|--|--|--|--|--|--|--|--|\n| men (years) | 67.1 | 68.9 | 70.3 | 71.7 | 72.4 | 73.5 | 75.3 |\n| women (years) | 76.1 | 77.8 | 78.6 | 79.5 | 79.9 | 80.3 | 81.1 |\nlet x be the number of years since 1970. what is the linear model for men?\ny = □x+□\n(round to three decimal places as needed.)

find linear models for each set of data. in what year will the two quantities be equal?\nlife expectancy at birth (1970 - 2000)\n| year | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 |\n|--|--|--|--|--|--|--|--|\n| men (years) | 67.1 | 68.9 | 70.3 | 71.7 | 72.4 | 73.5 | 75.3 |\n| women (years) | 76.1 | 77.8 | 78.6 | 79.5 | 79.9 | 80.3 | 81.1 |\nlet x be the number of years since 1970. what is the linear model for men?\ny = □x+□\n(round to three decimal places as needed.)

Answer

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:

$y = 0.360x+67.100$