Chapter 3.4, Problem 37E

To determine

To explain: whether the equations for horizontal and vertical lines can be written in

standard form or not.

Explanation of Solution

Given information:

Consider the line equation.

Calculation:

Let $a,b,c$ are the integers.

Consider the line equation $ax+by=c$

Find the equation for vertical line

  $\begin{array}{l}y=0\Rightarrow x=c/a=k\\ x=k\end{array}$

Find the equation for horizontal line

  $\begin{array}{l}x=0\Rightarrow y=c/b=k\\ y=k\end{array}$

Hence, the standard form horizontal and vertical lines are $y=k,x=k$

Hence, the equations for horizontal and vertical lines can be written in standard form.