Explanation Given Information: The provided equations of line are, 1 2 x + 3 4 y = 6 and − 3 2 x + y = 4 Explanation: Consider the provided equations of lines, 1 2 x + 3 4 y = 6 …… (1) − 3 2 x + y = 4 …… (2) Now, the slope-intercept form of line is, y = m x + b Where m is slope and b is y intercept. Now, convert the equation (1) into slope intercept form by adding − 1 2 x to both sides as, 1 2 x + 3 4 y − 1 2 x = 6 − 1 2 x 3 4 y = − 1 2 x + 6 Multiply both sides by 4 3 to get, y = − 2 3 x + 8 Thus, the slope is − 2 3 and the y intercept is ( 0 , 8 ) . Now, convert the equation (2) into slope intercept form by adding 3 2 x to both sides to get, − 3 2 x + 3 2 x + y = 4 + 3 2 x y = 3 2 x + 4 Thus, the slope is 3 2 and y intercept is ( 0 , 4 ) . Now, obtain the product of slopes of both the lines as, m 1 m 2 = − 2 3 ⋅ 3 2 = − 1 Since, the product of slopes is − 1 , so the lines are perpendicular. The following table represents the coordinates of the equation 1 2 x + 3 4 y = 6

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 9.6, Problem 24ES

To determine

Whether the graphs of the equations 12x+34y=6 and −32x+y=4 are perpendicular lines.

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Chapter 9.6, Problem 23ES

Chapter 9.6, Problem 25ES

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Chapter 9 Solutions

Developmental Mathematics (9th Edition)

Ch. 9.1 - Objective 8.1a: Determine whether a given number...Ch. 9.1 - Prob. 2SR Ch. 9.1 - Prob. 1DE Ch. 9.1 - Prob. 2DE Ch. 9.1 - Prob. 3DE Ch. 9.1 - Prob. 4DE Ch. 9.1 - Prob. 5DE Ch. 9.1 - Prob. 6DE Ch. 9.1 - Prob. 7DE Ch. 9.1 - Prob. 8DE

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Whether the graphs of the equations 1 2 x + 3 4 y = 6 and − 3 2 x + y = 4 are perpendicular lines.

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Whether the graphs of the equations 12x+34y=6 and −32x+y=4 are perpendicular lines.

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Chapter 9 Solutions