Chapter 13.3, Problem 1CE

a.

To determine

To find the slope of line $n$ if the slope of line $l$ is $2$ .

Answer to Problem 1CE

Explanation of Solution

Given:

Line $l$ is perpendicular to line $n$ .

  $m_l=2$ .

Calculation:

Since, it is given that the lines are perpendicular so the product of slope of these two line is $-1$ .

So,

  $\begin{array}{l}{m}_l\times m_n=-1\\ 2\times m_n=-1\\ m_n=-\frac{1}{2}\end{array}$

Therefore, the slope of line $n$ is $-\frac{1}{2}$ .

b.

To determine

To find the slope of line $n$ if the slope of line $l$ is $\frac{4}{5}$ .

Answer to Problem 1CE

The slope of line $n$ is $-\frac{5}{4}$ .

Explanation of Solution

Given:

Line $l$ is perpendicular to line $n$ .

  $m_l=\frac{4}{5}$ .

Calculation:

Since, it is given that the lines are perpendicular so the product of slope of these two line is $-1$ .

So,

  $\begin{array}{l}{m}_l\times m_n=-1\\ \frac{4}{5}\times m_n=-1\\ m_n=-\frac{5}{4}\end{array}$

Therefore, the slope of line $n$ is $-\frac{5}{4}$ .

c.

To determine

To find the slope of line $n$ if the slope of line $l$ is $-4$ .

Answer to Problem 1CE

The slope of line $n$ is $\frac{1}{4}$ .

Explanation of Solution

Given:

Line $l$ is perpendicular to line $n$ .

  $m_l=-4$ .

Calculation:

Since, it is given that the lines are perpendicular so the product of slope of these two line is $-1$ .

So,

  $\begin{array}{l}{m}_l\times m_n=-1\\ -4\times m_n=-1\\ m_n=\frac{1}{4}\end{array}$

Therefore, the slope of line $n$ is $\frac{1}{4}$ .

d.

To determine

To find the slope of line $n$ if the slope of line $l$ is not defined.

Answer to Problem 1CE

The slope of line $n$ is $0$ .

Explanation of Solution

Given:

Line $l$ is perpendicular to line $n$ .

  $m_l=\text{not defined}=\frac{1}{0}$ .

Calculation:

Since, it is given that the lines are perpendicular so the product of slope of these two line is $-1$ .

So,

  $\begin{array}{l}{m}_l\times m_n=-1\\ \frac{1}{0}\times m_n=-1\\ m_n=0\end{array}$

Therefore, the slope of line $n$ is $0$ .

e.

To determine

To find the slope of line $n$ id the slope of line $l$ is $0$ .

Answer to Problem 1CE

The slope of line $n$ is not defined.

Explanation of Solution

Given:

Line $l$ is perpendicular to line $n$ .

  $m_l=0$ .

Calculation:

Since, it is given that the lines are perpendicular so the product of slope of these two line is $-1$ .

So,

  $\begin{array}{l}{m}_l\times m_n=-1\\ 0\times m_n=-1\\ m_n=\frac{1}{0}=\text{not defined}\text{.}\end{array}$

Therefore, the slope of line $n$ is not defined.