Chapter 1.1, Problem 8E

(a)

To determine

To plot: The points $A\left(1,2\right)$ and $B\left(1,-3\right)$ .

Explanation of Solution

Given information: The two points for a line $L$ are $A\left(1,2\right)$ and $B\left(1,-3\right)$ .

Graph:

Plot the points $A\left(1,2\right)$ and $B\left(1,-3\right)$ on the coordinate plane as shown below.

  

Figure (1)

Interpretation: From the above graph it can be seen that the point A and B is 1 unit right to the y -axis.

(b)

To determine

To find: The slope of line $L$ .

Answer to Problem 8E

The slope of line $L$ is not defined.

Explanation of Solution

Given information: The two points for a line $L$ are $A\left(1,2\right)$ and $B\left(1,-3\right)$ .

Formula used: The formula for the slope of line determined by points $A\left(x_1,y_1\right)$ and $B\left(x_2,y_2\right)$ is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Substitute $1$ , $1$ for $x_1$ , $x_2$ and $2$ , $-3$ for $y_1$ , $y_2$ respectively in the formula for slope of line.

  $\begin{array}{c}m=\frac{-3-2}{1-1}\\ =\frac{-5}{0}\end{array}$

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

(c)

To determine

To graph: The line $L$ that passes through the points $A\left(1,2\right)$ and $B\left(1,-3\right)$ .

Explanation of Solution

Given information: The two points for a line $L$ are $A\left(1,2\right)$ and $B\left(1,-3\right)$ .

Graph:

The equation of vertical line passing through $\left(x_1,y_1\right)$ is $x=x_1$ .

Substitute $1$ for $x_1$ in the general equation for the equation of line $L$ .

  $\begin{array}{c}x=x_1\\ =1\end{array}$

So, the equation of the line $L$ is $x=1$ .

Draw the graph of the line $L$ as shown below on the coordinate plane.

  

Figure (2)

Interpretation: From the above graph it can be interpreted that the graph of the given line is parallel to the y -axis.