a. Answer y = − 3 4 x + 3 8 Explanation Given information: Write equations of the lines through the given point parallel to given line. 3 x + 4 y = 7 ( − 2 3 , 7 8 ) Calculation: Consider the given points on line. 3 x + 4 y = 7 ( − 2 3 , 7 8 ) The equation of line with slope m and given point on the line is, m = y − y 1 x − x 1 If the slopes of two non vertical lines are equal then lines are parallel. m 1 = m 2 If the slopes of two non vertical lines are negative reciprocal of each other then lines are perpendicular. m 1 = − 1 m 2 Now compare given line with standard equation of line, y = m x + c Where m is slope and c is intercept. 3 x + 4 y = 7 y = − 3 4 x + 7 4 m = − 3 4 A line parallel to the given line will have slope equal to the given line and it will pass through the given point ( − 2 3 , 7 8 ) So, y = m 1 x + c m 1 = m m 1 = − 3 4 y = − 3 4 x + c Substitute the given points in above eqation, y = − 3 4 x + c 7 8 = − 3 4 ( − 2 3 ) + c c = 3 8 y = − 3 4 x + 3 8 Hence the line is. y = − 3 4 x + 3 8 b. To determine Find equation of perpendicular line. Answer y = 4 3 x + 127 72 Explanation Given information: Write equations of the lines through the given point perpendicular to the given line.. 3 x + 4 y = 7 ( − 2 3 , 7 8 ) Calculation: Consider the given points on line. 3 x + 4 y = 7 ( − 2 3 , 7 8 ) The equation of line with slope m and given point on the line is, m = y − y 1 x − x 1 If the slopes of two non vertical lines are equal then lines are parallel. m 1 = m 2 If the slopes of two non vertical lines are negative reciprocal of each other then lines are perpendicular. m 1 = − 1 m 2 Now compare given line with standard equation of line, 3 x + 4 y = 7 y = m x + c Where m is slope and c is intercept. y = − 3 4 x + 7 4 m = − 3 4 A line perpendicular to the given line will have slope equal to the given line and it will pass through the given point ( − 2 3 , 7 8 ) So, y = m 2 x + c m 2 = − 1 m m 2 = 4 3 y = 4 3 x + c Substitute the given points in above eqation, y = 4 3 x + c 7 8 = 4 3 ( − 2 3 ) + c c = 127 72 y = 4 3 x + 127 72 Hence the line is. y = 4 3 x + 127 72

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 1.3, Problem 75E

To determine

Find equation of parallel line.

Expert Solution

Answer to Problem 75E

$y=−34x+38$

Explanation of Solution

Given information:

Write equations of the lines through the given point parallel to given line.

$3x+4y=7$

$(−23,78)$

Calculation:

Consider the given points on line.

$3x+4y=7$

$(−23,78)$

The equation of line with slope $m$ and given point on the line is,

$m=y−y1x−x1$

If the slopes of two non vertical lines are equal then lines are parallel.

$m1=m2$

If the slopes of two non vertical lines are negative reciprocal of each other then lines are perpendicular.

$m1=−1m2$

Now compare given line with standard equation of line,

$y=mx+c$ Where $m$ is slope and $c$ is intercept.

$3x+4y=7$

$y=−34x+74m=−34$

A line parallel to the given line will have slope equal to the given line and it will pass through the given point $(−23,78)$

So,

$y=m1x+cm1=mm1=−34y=−34x+c$

Substitute the given points in above eqation,

$y=−34x+c78=−34(−23)+cc=38y=−34x+38$

Hence the line is.

$y=−34x+38$

To determine

Find equation of perpendicular line.

Expert Solution

Answer to Problem 75E

$y=43x+12772$

Explanation of Solution

Given information:

Write equations of the lines through the given point perpendicular to the given line..

$3x+4y=7$

$(−23,78)$

Calculation:

Consider the given points on line.

$3x+4y=7$

$(−23,78)$

The equation of line with slope $m$ and given point on the line is,

$m=y−y1x−x1$

If the slopes of two non vertical lines are equal then lines are parallel.

$m1=m2$

If the slopes of two non vertical lines are negative reciprocal of each other then lines are perpendicular.

$m1=−1m2$

Now compare given line with standard equation of line,

$3x+4y=7$

$y=mx+c$ Where $m$ is slope and $c$ is intercept.

$y=−34x+74m=−34$

A line perpendicular to the given line will have slope equal to the given line and it will pass through the given point $(−23,78)$

So,

$y=m2x+cm2=−1mm2=43y=43x+c$

Substitute the given points in above eqation,

$y=43x+c78=43(−23)+cc=12772y=43x+12772$

Hence the line is.

$y=43x+12772$

Chapter 1.3, Problem 74E

Chapter 1.3, Problem 76E

Chapter 1 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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