Explanation Given Information: The provided equations of line are, y = − 2 3 x + 4 and 3 x + 2 y = 1 Explanation: Consider the provided equations of lines, y = − 2 3 x + 4 …… (1) 3 x + 2 y = 1 …… (2) Now, the slope-intercept form of line is, y = m x + b Where m is slope and b is y intercept. Now, for the equation (1), y = − 2 3 x + 4 The slope is − 2 3 and the y intercept is ( 0 , 4 ) . Now, convert the equation (2) into slope intercept form by adding − 3 x to both sides as, 3 x + 2 y − 3 x = 1 − 3 x 2 y = − 3 x + 1 Now, divide both sides by 2 to get, y = − 3 2 x + 1 2 Thus, the slope is − 3 2 and y intercept is ( 0 , 1 2 ) . 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 not − 1 , so the lines are not perpendicular. The following table represents the coordinates of the equation y = − 2 3 x + 4

16th Edition

ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Question

Chapter 9.6, Problem 16ES

To determine

Whether the graphs of the equations y=−23x+4 and 3x+2y=1 are perpendicular lines.

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Chapter 9.6, Problem 15ES

Chapter 9.6, Problem 17ES

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Chapter 9 Solutions

DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<

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 y = − 2 3 x + 4 and 3 x + 2 y = 1 are perpendicular lines.

Solution Summary: The author explains that the lines of the equations y=-23x+4 and 3x +2y =1 are not perpendicular.

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Whether the graphs of the equations y=−23x+4 and 3x+2y=1 are perpendicular lines.

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