Chapter 8.4, Problem 14E

To determine

To Find: Whether the graph of pair of equation is parallel, perpendicular or neither.

Answer to Problem 14E

Graph of Pair of equation is perpendicular.

Explanation of Solution

Given information:

The pair of equation:

  $\begin{array}{l}y=x+5\\ y=8-x\end{array}$

Formula used: -

Slope form of line: $y=mx+c$ .

Where $m$ is the slope of line, and $c$ is the $y$ -intercept when $x=0$ .

For parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$ .

For perpendicular lines with slope $m_1$ and $m_2$ , $m_1{m}_2=-1$ .

  $\begin{array}{l}y=x+5\\ y=8-x\end{array}$

Converting the pair of equation into Slope form of line: $y=mx+c$ .

  $y=x+5$

So, $m_1=1$

  $\begin{array}{l}y=8-x\\ y=-x+8\end{array}$

  $m_2=-1$

For parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$ .

  $1\ne -1$

  $m_1\ne m_2$

So, graph of Pair of equation is not parallel.

For perpendicular lines with slope $m_1$ and $m_2$ , $m_1{m}_2=-1$ .

  $\begin{array}{l}1\cdot -1=-1\\ -1=-1\end{array}$

  $m_1{m}_2=-1$

So, graph of Pair of equation is perpendicular.