Chapter SH, Problem 4.4MPS

(a)

To determine

To find:The slope of the lines approximating the path of each highway.

Answer to Problem 4.4MPS

The slope is $m_{80}=0.0625$ and $m_{70}=0.25$ .

Explanation of Solution

Given information: The given information is:

The points on highway $80$ are,

  $\left(1,9.75\right);\left(5,10\right)$

The points on highway $70$ are,

  $\left(2,1\right);\left(6,2\right)$

Calculation:

The slope of line is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

The slopeof highway $80$ is,

  $\begin{array}{l}{m}_{80}=\frac{y_2-y_1}{x_2-x_1}\\ m_{80}=\frac{10-9.75}{5-1}\\ m_{80}=\frac{0.25}{4}\end{array}$

  $m_{80}=0.0625$

The slope of highway $70$ is,

  $\begin{array}{l}{m}_{70}=\frac{y_2-y_1}{x_2-x_1}\\ m_{70}=\frac{2-1}{6-2}\\ m_{70}=\frac{1}{4}\end{array}$

  $m_{70}=0.25$

Therefore, the slope is $m_{80}=0.0625$ and $m_{70}=0.25$ .

(b)

To determine

To find:if the highways are parallel.

Answer to Problem 4.4MPS

The roads are not parallel.

Explanation of Solution

Given information: The given information is:

The points on highway $80$ are,

  $\left(1,9.75\right);\left(5,10\right)$

The points on highway $70$ are,

  $\left(2,1\right);\left(6,2\right)$

Calculation:

For two lines to be parallel, the slopes must be equal.

Since the slopes are $m_{80}=0.0625$ and $m_{70}=0.25$ .

Since the slopes are not equal hence they are not parallel.

Therefore, the roads are not parallel.