Chapter 1.1, Problem 7E

(a)

To determine

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

Explanation of Solution

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

Graph:

Plot the points $A\left(2,3\right)$ 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 is 2 units right from y -axis and point B is 1 unit left from y -axis.

(b)

To determine

To find: The slope of line $L$ .

Answer to Problem 7E

The slope of line $L$ is equal to $0$ .

Explanation of Solution

Given information: The two points for a line $L$ are $A\left(2,3\right)$ 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 $2$ , $-1$ for $x_1$ , $x_2$ and $3$ , $3$ for $y_1$ , $y_2$ respectively in the formula for slope of line.

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

Therefore, the slope of line $L$ is equal to $0$ .

(c)

To determine

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

Explanation of Solution

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

Graph:

The equation of line with slope $m$ and passing through the point $\left(x_1,y_1\right)$ is given by,

  $y=m\left(x-x_1\right)+y_1$

As calculated in part (b), the slope of the line $L$ is equal to $0$ and line passes through $\left(2,3\right)$ .

Substitute $2$ , $3$ for $x_1$ , $y_1$ and $0$ for $m$ in the general equation for the equation of line $L$ .

  $\begin{array}{c}y=0\left(x-2\right)+3\\ =0+3\\ =3\end{array}$

So, the equation of the line $L$ is $y=3$ .

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 line L is line parallel to x -axis.