Chapter 1.5, Problem 24E

To determine

To find: the standard form of line equation.

Answer to Problem 24E

  $y+11=0$

Explanation of Solution

Given information:

A line passes through $\left(4,-11\right)$ and parallel to $y=-9$ .

Calculation:

For $y=-9$ , the slope is zero. This line is horizontal.

Since, slope of two parallel lines are always equal. So, the slope (m) of both the lines is $0$ .

Put the coordinates and slope value in the slope intercept equation and solve as follows:

  $\begin{array}{c}y=mx+b\\ -11=\left(0\right)\left(4\right)+b\\ -11=0+b\\ b=-11\end{array}$

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

  $\begin{array}{l}m=-\frac{A}{B}\text{ and }b=-\frac{C}{B}\\ 0=-\frac{A}{B}\text{ and }-11=-\frac{C}{B}\left[\text{Put values of }m\text{ and }b\right]\\ \frac{0}{1}=\frac{A}{B}\text{ and }\frac{11}{1}=\frac{C}{B}\\ A=0,B=1\text{ and }C=11\left[\text{Simplify}\right]\end{array}$

Substitute the value of $A=-4,B=9\text{ and }C=183$ in the standard form of line as shown below.

  $\begin{array}{c}Ax+By+C=0\\ 0x+1y+11=0\\ y+11=0\end{array}$

Thus, the standard form of line is $y+11=0$ .