10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

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Expert Solution & Answer

Chapter P.4, Problem 42E

Solution

(a)

To Find:

Find an equation for the line passing through the point and parallel to the given line. Support your work graphically.

y=3x−1

Given information:

Point (−2, 3)

Line y=−2x+4

Concept used:

We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line. y=mx+b. Parallel lines have the same slope. The slope of the line with equation y=mx+b is b.

Calculation:

The given Point (-2, 3)

Line y=-2x+4

y=−2x+4point (−2,3)y=mx+b3=−2(2)+b3=4+bb=3−4b=−1so y=−2x−1

So the equation for the line passing through the point (−2, 3) and parallel to the given line is y=−2x−1

By graphically the graph of y=−2x+4 and y=−2x−1

(b)

To Find:

Find an equation for the line passing through the point and perpendicular to the given line. Support your work graphically.

y=x2+4

Given information:

Point (−2,3 )

Line y=−2x+4

Concept used:

We can write the equation of a line perpendicular to a given line if we know a point on the line and an equation of the given line. y−y1=m(x−x1) .

Calculation:

The given Point (−2,3 )

Line y=−2x+4

Here slope m-

m=−1−2m=12

y=−2x+4point (−2,3)y−y1=m(x−x1)y−3=12(x−(−2))y−3=x2+22y=x2+22+2y=x2+2+62y=x2+82y=x2+4

So the equation for the line passing through the point and perpendicular to the given line is y=x2+4

By graphically the graph of y=−2x+4 and y=x2+4

Chapter P.4, Problem 41E

Chapter P.4, Problem 43E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. P.1 - Prob. 1QR Ch. P.1 - Prob. 2QR Ch. P.1 - Prob. 3QR Ch. P.1 - Prob. 4QR Ch. P.1 - Prob. 5QR Ch. P.1 - Prob. 6QR Ch. P.1 - Prob. 7QR Ch. P.1 - Prob. 8QR Ch. P.1 - Prob. 9QR Ch. P.1 - Prob. 10QR

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Points, Lines, Planes, Segments, & Rays - Collinear vs Coplanar Points - Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=dDWjhRfBsKM;License: Standard YouTube License, CC-BY

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Solution Summary: The author explains how to find an equation for the line passing through the point and perpendicular to the given line.

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Chapter P Solutions