Explanation Procedure used: 1. Solve the given equation for y and compute the slope m from the that equation. 2. The slope of the perpendicular line and the given line are negative reciprocal to each other. 3. Obtain the point-slope form of the straight line by substituting the value of m x 1 and y 1 in y − y 1 = m ( x − x 1 ) . 4. Express the equation in slope intercept form y = m x + b or in the standard form A x + B y = C . Calculation: From the given information, the values of x 1 and y 1 are 3 and − 1 , respectively. Compute the equation of the perpendicular line as follows. Solve the given equation 2 x + 3 y = 4 for y as follows. 3 y = − 2 x + 4 y = − 2 x + 4 3 y = − 2 x 3 + 4 3 Compare the above equation with the slope-intercept form y = m x + b and obtain the value of m . y = m ↓ x + b y = − 2 3 x + 4 3 From the above equation, the value of m given is − 2 3 . Obtain the slope of the perpendicular line as follows. Since the slopes of perpendicular lines are negative reciprocal to each other obtain the negative reciprocal of − 2 3 . m perpendicular = − ( 1 ( − 2 3 ) ) = − ( 3 − 2 ) = 3 2 Thus, m perpendicular is 3 2 . Now substitute x 1 = 3 , y 1 = − 1 and m = 3 2 , in y − y 1 = m ( x − x 1 )

MML F/COLLEGE MAT F/TRADES - ACCESS CODE

10th Edition

ISBN: 9781323845967

Author: Hobbs

Publisher: PEARSON

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Chapter 9.4, Problem 47E

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The standard form of the equation that is perpendicular to the line 2x+3y=4 and passes through the point (3,−1).

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Chapter 9.4, Problem 46E

Chapter 9.4, Problem 48E

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MML F/COLLEGE MAT F/TRADES - ACCESS CODE

Ch. 9.1 - Find y if x = 4 in the equation 3x + 2y = 6. Ch. 9.1 - Locate the points in Fig. 9–12 by giving the...Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E

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The standard form of the equation that is perpendicular to the line 2 x + 3 y = 4 and passes through the point ( 3 , − 1 ) .

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The standard form of the equation that is perpendicular to the line 2x+3y=4 and passes through the point (3,−1).

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Chapter 9 Solutions