Chapter 1.3, Problem 71E

To determine

Find either a line is parallel or perpendicular.

Answer to Problem 71E

The lines are parallel.

Explanation of Solution

Given information:

Determine whether the lines $L_1$ and $L_2$ passing through the pairs of points are parallel, perpendicular, or neither.

  $L_1:\left(3,6\right),\left(-6,0\right)$

  $L_2:\left(0,-1\right),\left(5,\frac{7}{3}\right)$

Calculation:

Consider the given points on line.

  $L_1:\left(3,6\right),\left(-6,0\right)$

  $L_2:\left(0,-1\right),\left(5,\frac{7}{3}\right)$

If the slope $m$ of line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is,

  $m=\frac{y_2-y_1}{x_2-x_1}$

If the slopes of two non vertical lines are equal then lines are parallel.

  $m_1=m_2$

If the slopes of two non vertical lines are negative reciprocal of each other then lines are perpendicular.

  $m_1=-\frac{1}{m_2}$

  $\begin{array}{l}{m}_{L1}=\frac{0-6}{-6-3}\\ =\frac{2}{3}\\ m_{L2}=\frac{\frac{7}{3}-\left(-1\right)}{5-0}\\ =\frac{2}{3}\end{array}$

  $m_{L1}=m_{L2}$

The slopes of two non vertical lines are equal then lines are parallel

Hence the lines are parallel.