PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.4, Problem 41E
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 (1, 2)

Line y=3x-2

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 (1, 2)

Line y=3x-2

  y=3x−2point (1,  2)y=mx+b2=3(1)+b2=3+bb=2−3b=−1so y=3x−1

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

By graphically the graph of y=3x−2 and y=3x−1

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 41E , additional homework tip 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=−x3+73

Given information:

Point (1, 2)

Line y=3x-2

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 (1, 2)

Line y=3x-2

Here slope m=−13

  y=3x−2point (1,  2)y−y1=m(x−x1)y−2=−13(x−1)y−2=−x3+13y=−x3+13+2y=−x3+1+63y=−x3+73

So the equation for the line passing through the point and perpendicular to the given line is y=−x3+73

By graphically the graph of y=3x−2 and y=−x3+73

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 41E , additional homework tip 2

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Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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