Chapter 8.4, Problem 31WE

To determine

To Show:The given lines are parallel.

Explanation of Solution

Given information:

The equation of lines:

  $\begin{array}{l}2x-3y=7\\ -2x+3y=4\end{array}$

Formula used:

Slope-intercept line: $y=mx+c$ .

Where m is slope of line, and c is y-intercept of line.

Slope of parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$

  $\begin{array}{l}2x-3y=7\\ -2x+3y=4\end{array}$

Convert both equations to slope-intercept form:

Recall Slope-intercept line: $y=mx+c$ .

Where m is slope of line, and c is y-intercept of line.

  $\begin{array}{l}2x-3y=7\\ -3y=-2x+7\\ y=\frac{-2}{-3}x+\left(\frac{7}{-3}\right)\\ y=\frac{2}{3}x+\left(-\frac{7}{3}\right)\end{array}$

  $m_1=\frac{2}{3}$

  $\begin{array}{l}-2x+3y=4\\ 3y=2x+4\\ y=\frac{2}{3}x+\frac{4}{3}\end{array}$

  $m_2=\frac{2}{3}$

As we know, Slope of parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$

  $\begin{array}{l}\frac{2}{3}=\frac{2}{3}\\ m_1=m_2\end{array}$

Hence, Both of the line of given equation are parallel.