Chapter 13.2, Problem 7PSA

(a)

To determine

To find: The slope of line $\overleftrightarrow{\text{AB}}$ .

Answer to Problem 7PSA

The slope of line $\overleftrightarrow{\text{AB}}$ is 1.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the slope of line $\overleftrightarrow{\text{AB}}$ as follows.

Substitute $2$ for $x_1$ , 6 for $x_2$ , $11$ for $y_2$ and $7$ for $y_1$ in the equation $m=\frac{y_2-y_1}{x_2-x_1}$ .

  $\begin{array}{c}m=\frac{11-7}{6-2}\\ =\frac{4}{4}\\ =1\end{array}$

Therefore, the slope of line $\overleftrightarrow{\text{AB}}$ is 1.

(b)

To determine

To find: The equation of line $\overleftrightarrow{\text{AB}}$ .

Answer to Problem 7PSA

The equation of line $\overleftrightarrow{\text{AB}}$ is $y=x+5$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the y-intercept as follows.

Substitute 1 for $m$ , 6 for $x$ , and 11 for $y$ in the equation $y=mx+b$ .

  $\begin{array}{c}11=1\left(6\right)+b\\ 11-6=b\\ 5=b\end{array}$

Substitute 1 for $m$ , and 5 for $b$ in the equation $y=mx+b$ .

  $\begin{array}{c}y=\left(1\right)x+5\\ =x+5\end{array}$

Therefore, the equation of line $\overleftrightarrow{\text{AB}}$ is $y=x+5$ .

(c)

To determine

To find: The slope of line $\overleftrightarrow{\text{CD}}$ .

Answer to Problem 7PSA

The slope of line $\overleftrightarrow{\text{CD}}$ is $-\frac{1}{2}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the slope of line $\overleftrightarrow{\text{CD}}$ as follows.

Substitute $1$ for $x_1$ , $7$ for $x_2$ , $-6$ for $y_2$ and $-3$ for $y_1$ in the equation $m=\frac{y_2-y_1}{x_2-x_1}$ .

  $\begin{array}{c}m=\frac{\left(-6\right)-\left(-3\right)}{7-1}\\ =\frac{-3}{6}\\ =-\frac{1}{2}\end{array}$

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

(d)

To determine

To find: The equation of line $\overleftrightarrow{\text{CD}}$ .

Answer to Problem 7PSA

The equation of line $\overleftrightarrow{\text{CD}}$ is $y=-\frac{1}{2}x-\frac{5}{2}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the y-intercept as follows.

Substitute $-\frac{1}{2}$ for $m$ , 1 for $x$ , and $-3$ for $y$ in the equation $y=mx+b$ .

  $\begin{array}{c}-3=-\frac{1}{2}\left(1\right)+b\\ -3+\frac{1}{2}=b\\ -\frac{5}{2}=b\end{array}$

Substitute $-\frac{1}{2}$ for $m$ , and $-\frac{5}{2}$ for $b$ in the equation $y=mx+b$ .

  $y=-\frac{1}{2}x-\frac{5}{2}$

Therefore, the equation of line $\overleftrightarrow{\text{CD}}$ is $y=-\frac{1}{2}x-\frac{5}{2}$ .