Chapter 1.5, Problem 27E

To determine

To find: the standard form of equation for line.

Answer to Problem 27E

  $y+13=0$

Explanation of Solution

Given information:

Let the line whose standard equation needs to be evaluated be $l$ .

Line $l$ is $\perp$ to the graph of equation $x=12$ .

Line $l$ passes through $\left(6,-13\right)$ .

Calculation:

Compare $x=0$ with the slope intercept equation and evaluate the slope as shown below.

  $\begin{array}{c}y=mx+b\\ y=m\left(0\right)+b\\ y-b=m\left(0\right)\\ m=\frac{y-b}{0}\\ =\text{undefined}\end{array}$

The slope of given line is undefined. So, this line is a vertical line.

The slope of line $l$ perpendicular to $x=0$ can be evaluated as follows:

  $\begin{array}{l}\perp m=-\frac{1}{m}\\ =-\frac{1}{\text{undefined}}\left[\text{Substituting value of }m\right]\\ =0\end{array}$

Let’s put the value of m and $\left(6,-13\right)$ in the slope intercept formula and evaluate value of b as follows:

  $\begin{array}{c}y=mx+b\\ -13=\left(0\right)\left(6\right)+b\\ -13=0+b\\ b=-13\end{array}$

Now, substitute the value of m and b in the slope intercept formula and find the equation as follows:

  $\begin{array}{l}y=mx+b\\ y=\left(0\right)x+\left(-13\right)\\ y=0-13\\ y+13=0\left[\begin{array}{l}\text{Rearranging in standard form}\\ \text{i}\text{.e}\text{. }Ax+By+b=0\end{array}\right]\end{array}$

Thus, the standard form equation of line $l$ is $y+13=0$ .