(a) Explanation Result used: The lines are parallel if they have same slope. That is, m 1 = m 2 . Proof: The given lines are a x + b y + c = 0 and a x + b y + d = 0 . Write the given equation a x + b y + c = 0 in slope-intercept form. a x + b y + c = 0 b y = − a x − c y = − a b x − c b Thus, the slope of the equation a x + b y + c = 0 is m 1 = − a b . Write the given equation a x + b y + d = 0 in slope-intercept form (b) To determine To show: The lines a x + b y + c = 0 and b x − a y + d = 0 are perpendicular for nonzero values of a , b , c and d .

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 21.2, Problem 45E

(a)

To determine

To show: The lines ax+by+c=0 and ax+by+d=0 are parallel for nonzero values of a, b, c and d.

(b)

To determine

To show: The lines ax+by+c=0 and bx−ay+d=0 are perpendicular for nonzero values of a, b, c and d.

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Chapter 21.2, Problem 44E

Chapter 21.2, Problem 46E

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The lines a x + b y + c = 0 and a x + b y + d = 0 are parallel for nonzero values of a , b , c and d .