Chapter 7.7, Problem 28E

a.

To determine

To find:for whom predicted equation is a better predictor.

Answer to Problem 28E

Linda

Explanation of Solution

Given information:

The equation below represents the systolic blood pressure $\left(y\right)$ of a person to their age $\left(x\right)$ .

  $4x-3y+228=0$

Person	Age $\left(x\right)$	Systolic blood pressure $\left(y\right)$
Linda	19	112
Her father	45	120

The figure is shown below.

  

Calculation:

Put the details of Lindain the equation given below and solve as follows:

  $\begin{array}{c}d=\left|\frac{A{x}_1+B{y}_1+C}{\sqrt{A^2+B^2}}\right|\left[\text{Put }x=19\text{ and }y=112\right]\\ =\left|\frac{4\left(19\right)-3\left(112\right)+228}{\sqrt{4^2+3^2}}\right|\\ =\frac{32}{5}\\ =6.4\end{array}$

Put the details of Linda’s father in the equation given below and solve as follows:

  $\begin{array}{c}d=\left|\frac{A{x}_1+B{y}_1+C}{\sqrt{A^2+B^2}}\right|\left[\text{Put }x=45\text{ and }y=120\right]\\ =\left|\frac{4\left(45\right)-3\left(120\right)+228}{\sqrt{4^2+3^2}}\right|\\ =\frac{48}{5}\\ =9.6\end{array}$

Thus, the predicted equation is a better predictor for Linda.

b.

To determine

To find:the initial age required to predict the mild hypertension by referring the graph.

Answer to Problem 28E

48 years

Explanation of Solution

Given information:

The equation below represents the systolic blood pressure $\left(y\right)$ of a person to their age $\left(x\right)$ .

  $4x-3y+228=0$

The figure is shown below.

  

Calculation:

The graph states that at $y=140$ , the state is of mild hypertension.

Substitute $y=140$ and evaluate $x$ as shown below.

  $\begin{array}{c}4x-3\left(140\right)+228=0\\ 4x=192\\ x=48\end{array}$

Thus, the initial age required to predict the mild hypertension is 48 years.