To determine The equation of the given line L . Explanation Given: The line L contains a point ( 1 , 2 ) and it is perpendicular to the line y = 2 x . Definition used: 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 .” The point slope form of an equation of a line: An equation of a non-vertical line with slope m that contains the point ( x 1 , y 1 ) is y − y 1 = m ( x − x 1 ) . Calculation: Since the equation of the line is perpendicular to the line y = 2 x , the slope of both the lines will be opposite reciprocal of each other. Compare the equation of the line y = 2 x with the slope intercept form. y = m ↓ x + b y = 2 x Thus, the slope of the equation y = 2 x is 2

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 45AYU

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The equation of the given line L.

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Chapter F.3, Problem 44AYU

Chapter F.3, Problem 46AYU

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College Algebra: Concepts Through Functions (4th Edition)

Ch. F.1 - Prob. 1AYU Ch. F.1 - If −3 and 5 are the coordinates of two points on...Ch. F.1 - If 3 and 4 are the legs of a right triangle, the...Ch. F.1 - Use the converse of the Pythagorean Theorem to...Ch. F.1 - The area A of a triangle whose base is b and whose...Ch. F.1 - True or False Two triangles are congruent if two...Ch. F.1 - Prob. 7AYU Ch. F.1 - The coordinate axes divide the xy-plane into four...Ch. F.1 - If three distinct points P, Q, and R all lie on a...Ch. F.1 - True or False The distance between two points is...

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