Chapter 4.3, Problem 22PPS

To determine

To find: the whether the graphs of the following equations are parallel or perpendicular.

Answer to Problem 22PPS

Since $m_1=m_2=m_3$ equations $3x-9y=9,3y=x+12,2x-6y=12$ are parallel to each other.

Explanation of Solution

Given information:

Given equations are

1. $3x-9y=9$
2. $3y=x+12$
3. $2x-6y=12$

Calculation:

  $y=mx+b$ is the slope intercept form of the line.

Consider the first equation

  $\begin{array}{c}3x-9y=9\\ 9y=3x-9\\ \frac{9y}{9}=\frac{3x}{9}-\frac{9}{9}\\ y=\frac{1}{3}x-1\end{array}$

Therefore, slope $\left(m_1\right)=\frac{1}{3}$ .

Consider the second equation

  $\begin{array}{c}3y=x+12\\ \frac{3y}{3}=\frac{x}{3}+\frac{12}{3}\\ y=\frac{1}{3}x+4\end{array}$

Therefore slope $\left(m_2\right)=\frac{1}{3}$

Consider the third equation

  $\begin{array}{c}2x-6y=12\\ 6y=2x-12\\ \frac{6y}{6}=\frac{2x}{6}-\frac{12}{6}\\ y=\frac{1}{3}x-2\end{array}$ .

Therefore slope $\left(m_3\right)=\frac{1}{3}$

Since $m_1=m_2=m_3$ equations $3x-9y=9,3y=x+12,2x-6y=12$ are parallel to each other.