Chapter 1, Problem 6CR

(a)

To determine

To find:

An equation of a line using the following point and slope of the line:

  $\left(-2,6\right),m=0$

Answer to Problem 6CR

An equation of a line is $y=6$ .

Explanation of Solution

Given information:

  $\begin{array}{l}\left(x_1,y_1\right)=\left(-2,6\right)\\ m=0\end{array}$

Formula used:

An equation of a line passing through a point with slope is given by the following expression:

  $\left(y-y_1\right)=m\left(x-x_1\right)$

Calculation:

An equation of a line passing through a point $\left(-2,6\right)$ with slope $\left(m=0\right)$ is given by the following expression:

  $\left(y-y_1\right)=m\left(x-x_1\right)$

Put the given data:

  $\begin{array}{l}\left(y-6\right)=0\left(x+2\right)\\ y-6=0\\ y=6\end{array}$

(b)

To determine

Three additional points through which the line passes.

Answer to Problem 6CR

Three additional points through which the line passes are $\left(0,6\right),\left(-2,6\right),\left(2,6\right)$

Explanation of Solution

Given information:

From sub-part (a):

The equation of line is $y=6$

Calculation:

An equation of a line passing through a point $\left(-2,6\right)$ with slope $\left(m=0\right)$ is given by the following expression:

  $y=6$

The line equation is graphed as below:

  

From the graph:

Three additional points through which the line $\left(y=6\right)$ passes are

  $\left(0,6\right),\left(-2,6\right),\left(2,6\right)$ .