Chapter 8.9, Problem 6PPS

(a)

To determine

To calculate: To write an equation in slope-intercept form of the line of the fit of the data

Answer to Problem 6PPS

Theequation in slope-intercept form of the line of the fit of the data is $y=\frac{3}{20}x-223$

Explanation of Solution

Given information: The life expectancy of someone born in 2020 is $77.0$ years. The life expectancy of someone born in $2010$ is $78.5$ years

Formula Used:

Equation of line passing through two points is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Calculation:

Given that life expectancy of someone born in 2020 is $77.0$ years. The life expectancy of someone born in $2010$ is $78.5$ years

Thus, points satisfying the line of fit is as follows:

  $\left(2000,77\right)$ and $\left(2010,78.5\right)$

Using two points form of line, equation of line is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Substituting the values in above equation,

  $\begin{array}{l}y-77=\frac{78.5-77}{2010-2000}\left(x-2000\right)\\ y-77=\frac{1.5}{10}\left(x-2000\right)\\ y-77=\frac{3}{20}\left(x-2000\right)\\ 20y-1540=3x-6000\\ 20y=3x-4460\\ y=\frac{3}{20}x-223\end{array}$

Conclusion:

Hence, the equation of line is $y=\frac{3}{20}x-223$

(b)

To determine

To calculate: To predict the life expectancy of a person born in $2015$

Answer to Problem 6PPS

Thelife expectancy in 2015 is $79.25$ years

Explanation of Solution

Given information: The life expectancy of someone born in 2020 is $77.0$ years. The life expectancy of someone born in $2010$ is $78.5$ years

Formula Used:

Equation of line passing through two points is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Calculation:

Given that life expectancy of someone born in 2020 is $77.0$ years. The life expectancy of someone born in $2010$ is $78.5$ years

Now, equation in slope-intercept form of the line of the fit of the data is $y=\frac{3}{20}x-223$

In order to calculate the life expectancy in year $2015$ , substitute $x=2015$ in above equation

  $\begin{array}{l}y=\frac{3}{20}\left(2015\right)-223\\ y=302.25-223\\ y=79.25\end{array}$

Conclusion:

Hence, the life expectancy in 2015 is $79.25$ years