   # The properties in Problem 83 provide us with another way to write the equation of a line parallel or perpendicular to a given line that contains a given point not on the line. For example, suppose that we want the equation of the line perpendicular to 3 x + 4 y = 6 that contains the point ( 1 , 2 ) . The form 4 x − 3 y = k , where k is a constant, represents a family of lines perpendicular to 3 x + 4 y = 6 because we have satisfied the condition A A ′ = − B B ′ . Therefore, to find what specific line of the family contains ( 1 , 2 ) , we substitute 1 for x and 2 for y to determine k. 4 x − 3 y = k 4 ( 1 ) − 3 ( 2 ) = k − 2 = k Thus the equation of the desired line is 4 x − 3 y = − 2 . Use the properties from Problem 83 to help write the equation of each of the following lines. (a) Contains ( 1 , 8 ) and is parallel to 2 x + 3 y = 6 . (b) Contains ( − 1 , 4 ) and is parallel to x − 2 y = 4 . (c) Contains ( 2 , − 7 ) and is perpendicular to 3 x − 5 y = 10 . (c) Contains ( − 1 , − 4 ) and is perpendicular to 2 x + 5 y = 12 . ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 7.4, Problem 84PS
Textbook Problem
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## The properties in Problem 83 provide us with another way to write the equation of a line parallel or perpendicular to a given line that contains a given point not on the line. For example, suppose that we want the equation of the line perpendicular to 3 x + 4 y = 6 that contains the point ( 1 ,   2 ) . The form 4 x − 3 y = k , where k is a constant, represents a family of lines perpendicular to 3 x + 4 y = 6 because we have satisfied the condition A A ′ = − B B ′ . Therefore, to find what specific line of the family contains ( 1 ,   2 ) , we substitute 1 for x and 2 for y to determine k. 4 x − 3 y = k 4 ( 1 ) − 3 ( 2 ) = k − 2 = k Thus the equation of the desired line is 4 x − 3 y = − 2 .Use the properties from Problem 83 to help write the equation of each of the following lines.(a) Contains ( 1 , 8 ) and is parallel to 2 x + 3 y = 6 .(b) Contains ( − 1 , 4 ) and is parallel to x − 2 y = 4 .(c) Contains ( 2 , − 7 ) and is perpendicular to 3 x − 5 y = 10 .(c) Contains ( − 1 , − 4 ) and is perpendicular to 2 x + 5 y = 12 .

To determine

(a)

To verify:

The equation of lines that is parallel to given line and contains the given point.

### Explanation of Solution

Given:

The given lines is,

2x+3y=6

The given point is,

(1,8)

The given property states the following.

If AA=BBCC, then the lines are parallel.

Approach:

Slope-Intercept Form of an equation is,

y=mx+b

Where, m is the slope of the line and b is the y intercept of the line.

Calculation:

The given line is,

2x+3y=6...(1)

Consider the form of line parallel to the line in equation (1) to be,

2x+3y=k...(2)

Where, k is the constant other than 6.

The given relation is,

AA=BBCC..

To determine

(b)

To verify:

The equation of lines that is parallel to given line and contains the given point.

To determine

(c)

To verify:

The equation of lines that is perpendicular to given line and contains the given point.

To determine

(d)

To verify:

The equation of lines that is perpendicular to given line and contains the given point.

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