Chapter 1, Problem 52SGA

To determine

To find: the standard form of line equation.

Answer to Problem 52SGA

  $y+6=0$

Explanation of Solution

Given information:

  $x=-8$

Coordinates = $\left(4,-6\right)$

Calculation:

For, $x=-8$ ,the slope is undefined because this line is vertical.

A line perpendicular to line of equation, $x=-8$ , will be horizontal. So, the slope of line can be evaluated as follows:

  $\begin{array}{c}\perp m=-\frac{1}{m}\\ undefined=-\frac{1}{m}\\ m=-\frac{1}{undefined}\\ =0\end{array}$

Put the coordinates and slope value of line A, in the slope intercept equation and solve as follows:

  $\begin{array}{c}y=mx+b\\ -6=\left(0\right)\left(4\right)+b\\ -6=0+b\\ b=-6\end{array}$

Equations for converting the slope and y-intercept into standard form as follows:

  $\begin{array}{l}m=-\frac{A}{B}\text{ and }b=-\frac{C}{B}\\ 0=-\frac{A}{B}\text{ and }-6=-\frac{C}{B}\left[\text{Put values of }m\text{ and }b\right]\\ 0=\frac{A}{B}\text{ and 6}=\frac{C}{B}\left[\text{Simplify}\right]\\ \frac{0}{1}=\frac{A}{B}\text{ and }\frac{6}{1}=\frac{C}{B}\left[\text{Finding common denominator}\right]\end{array}$

The value of $A=0,B=1,\text{ and }C=6$ .

Substitute the value of $A,B\text{ and }C$ in the standard form of line as shown below.

  $\begin{array}{c}Ax+By+C=0\\ 0x+1y+6=0\\ 0+y+6=0\\ y+6=0\end{array}$

Thus, the standard form of line is $y+6=0$ .