Chapter 4.4, Problem 15E

(a)

To determine

To write the equation that models the birth rate as a function of the number of years since $1960$ .

  

Answer to Problem 15E

Theequation that models the birth rate as a function of the number of years since $1960$ is $y=-0.18x+35.4$ .

Explanation of Solution

Given:

  

Formula Used:

The equation of a line is written as $y=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Given:

  

Plotting the above points on a graph, we have:

  

The above points represent approximately a straight line.

Thus,

Slope $=$$m=\frac{y_2-y_1}{x_2-x_1}$

  $m=\frac{33.6-35.4}{10-0}$

  $m=-0.18$

Thus, the equation of the line is

  $y-y_1=m\left(x-x_1\right)$

  $\begin{array}{l}y-35.4=-0.18\left(x-0\right)\\ y-35.4=-0.18x\\ y=-0.18x+35.4\end{array}$

Thus, the equation that models the birth rate as a function of the number of years since $1960$ is $y=-0.18x+35.4$ .

Conclusion:

Theequation that models the birth rate as a function of the number of years since $1960$ is $y=-0.18x+35.4$ .

(b)

To determine

To interpret the slope and $y$ -intercept of the line of fit.

  

Answer to Problem 15E

The Slope is $-0.18$ and $y$ -intercept is $35.4$ .

Explanation of Solution

Given:

  

Formula Used:

The equation of a line is written as $y=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Given:

  

Equation that models the birth rate as a function of the number of years since $1960$ is $y=-0.18x+35.4$

  Slope $=$$m=-0.18$

  $y$ -intercept $=$$b$$=$$35.4$ .

Conclusion:

The Slope is $-0.18$ and $y$ -intercept is $35.4$ .