## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 769: 117

#### Answer

The slopes of the provided two lines are equal.

#### Work Step by Step

If the slopes of two lines are equal then the lines are parallel to each other. The slope $\left( m \right)$ of the line passing through the two points $\left( {{x}_{1}},{{x}_{2}} \right)\text{ and }\left( {{y}_{1}},{{y}_{2}} \right)$ is given by: $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$. The slope of the first line passing through the point $\left( -3,-3 \right)$ and $\left( 0,3 \right)$ is: \begin{align} & {{m}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & =\frac{3-\left( -3 \right)}{0-\left( -3 \right)} \\ & =\frac{6}{3} \\ & =2 \end{align} So, the slope of the first line is $2$ The slope of the second line passing through $\left( 0,0 \right)$ and $\left( 3,6 \right)$ is \begin{align} & {{m}_{2}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & =\frac{0-\left( -6 \right)}{0-\left( -3 \right)} \\ & =\frac{6}{3} \\ & =2 \end{align} Thus, the slope of the second line is also $2$.

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