Chapter 1.1, Problem 82E

To determine

To Identify: The relationship that exists among the lines then use a graphing utility to graph the equations in the same window. Adjust the viewing window so that the slope exists appear correct. Use the slopes to verify the results.

Answer to Problem 82E

  

Explanation of Solution

Given: $(a)y=\frac{2}{3}x$

  $(b)y=-\frac{3}{2}x$

  $(c)y=\frac{2}{3}x+2$

Given: $(a)y=\frac{2}{3}x$

  $(b)y=-\frac{3}{2}x$

  $(c)y=\frac{2}{3}x+2$

The graph of the function is

  

Lines having the same slope are parallel

All perpendicular lines have slopes that are negative reciprocal to one another.

From the graph it is concluded that

The slope of line $(a)y=\frac{2}{3}x$$(m_1)$ is $\frac{2}{3}$

The slope of $(b)y=-\frac{3}{2}x$$(m_2)$ is $-\frac{3}{2}$

The slope of line $(c)y=\frac{2}{3}x+2$$(m_3)$ is $\frac{2}{3}$$(m_1)=(m_3)$

The lines are parallel

  $m_2=-\frac{1}{m_1}or-\frac{1}{m_3}$

The line

  $y=-\frac{3}{2}x$ is perpendicular to both lines $y=\frac{2}{3}x$ and $y=\frac{2}{3}x+2$