Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 31: 106

Answer

The two lines are neither parallel nor perpendicular.

Work Step by Step

If two non-vertical and non-horizontal lines are parallel, then their slopes are equal. If two non-vertical and non-horizontal lines are perpendicular, then the product of their slopes is $-1$. Here, for the first line: $y=-2x+3$ The slope, in this form of the equation, is equal to the coefficient of $x$. Hence, the slope of this line is $-2$. For the second line: $y=-\frac{1}{2}x+2$ The slope of this line is $-\frac{1}{2}$ The slopes are not equal and their product is not $-1$. Therefore the two lines are neither parallel nor perpendicular.
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