Explanation Given Information: The provided equation of the lines are 3 x − 4 y = 12 and 8 x − 6 y = 15 . The slope-intercept form of the line, y = m x + c Where, m is the slope of the line and c is the intercept on y -axis. Parallel lines: The two lines, L 1 : y = m 1 x + c 1 and L 2 : y = m 2 x + c 2 are parallel only when the slope of these two lines are equal or both the lines are perpendicular to x -axis the that is, m 1 = m 2 Perpendicular lines: The two lines, L 1 : y = m 1 x + c 1 and L 2 : y = m 2 x + c 2 are perpendicular only when the multiplication of the slope of these two lines are equal to − 1 that is, m 1 m 2 = − 1 If one line is vertical with equation x = a then other line is horizontal with equation y = b . Consider the provided equations of the line, 3 x − 4 y = 12 and 8 x − 6 y = 15 In order to determine whether the equation of the lines is parallel, perpendicular or neither calculate the slope of the lines. Consider the first equation, 3 x − 4 y = 12 Write the equation 3 x − 4 y = 12 in slope intercept form as, Subtract, 3 x on both the sides of the equation 3 x − 4 y = 12 , 3 x − 4 y − 3 x = − 3 x + 12 − 4 y = − 3 x + 12 Multiply by ( − 1 4 ) on both the sides of the equation − 4 y = − 3 x + 12 , − 1 4 ( − 4 y ) = − 1 4 ( − 3 x + 12 ) y = 3 4 x − 12 4 = 3 4 x − 3 Thus, y = 3 4 x − 3 Now, compare the equation y = 3 4 x − 3 with standard slope-intercept form of the equation y = m x + c

12th Edition

ISBN: 9781337630580

Author: Dale Ewen

Publisher: Cengage Learning

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Chapter 8, Problem 27R

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Whether the equation of the lines 3x−4y=12 and 8x−6y=15 are perpendicular, parallel or neither.

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Chapter 8, Problem 26R

Chapter 8, Problem 28R

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Whether the equation of the lines 3 x − 4 y = 12 and 8 x − 6 y = 15 are perpendicular, parallel or neither.

Solution Summary: The author calculates whether the equation of the lines is parallel, perpendicular, or neither.

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Whether the equation of the lines 3x−4y=12 and 8x−6y=15 are perpendicular, parallel or neither.

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Chapter 8 Solutions