Explanation Given: The equation of two lines are y = − 2 x + 3 and y = − 1 2 x + 2 . Definition used: Parallel line: The non-vertical lines are said to be parallel if and only if the slopes of these lines are equal with different y -intercept. Perpendicular line: The non-vertical lines are said to be perpendicular if and only if the product of their slope is −1. That is, m 1 ⋅ m 2 = − 1 m 2 = − 1 m 1 Here m 1 and m 2 are the slopes of the line perpendicular to each other. Theorem used: “ Slope-intercept form of an equation of a line: An equation of a line with slope m and y -intercept b is y = m x + b .” Calculation: Compute the slope m 1 of the equation y = − 2 x + 3 as follows. Compare the equation y = − 2 x + 3 with the slope intercept form. y = m 1 ↓ x + b 1 ↓ y = − 2 x + 3 That is, the coefficient of x , −2 is the slope and the constant, 3 is y intercept. Thus, m 1 is −2 and b 1 is 3

College Algebra: Concepts Through Functions (4th Edition)

4th Edition

ISBN: 9780134686967

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Chapter F.3, Problem 108AYU

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Whether the given the equations of lines are parallel, perpendicular or neither.

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Chapter F.3, Problem 107AYU

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College Algebra: Concepts Through Functions (4th Edition)

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