a. Answer 3 x − y − 2 = 0 Explanation Given information: The line equation ( l ) is as follows: 3 x − y = 10 Condition: Line is parallel to l and passes through ( 0 , − 2 ) . Calculation: Rearrange the given line equation in terms of y and compare it with the slope intercept formula as follows: y = 3 x − 10 y = m x + b ∴ m = 3 , b = − 10 If two lines are parallel, then the slope value of both the lines is same, i.e. 3 Put the given points ( 0 , − 2 ) in the slope intercept formula and evaluate b as follows: y = m x + b − 2 = 3 ( 0 ) + b − 2 = b Thus, the y- intercept for the line parallel to l is − 2 . Now, substitute the value of m and b in the standard form of line equation as follows: y = m x + b y = 3 x − 2 3 x − y − 2 = 0 Therefore, the standard form of line equation is 3 x − y − 2 = 0 . b. To determine To find: the standard form of line equation at given condition. Answer x + 3 y + 6 = 0 Explanation Given information: The line equation ( l ) is as follows: 3 x − y = 10 Condition: Line is perpendicular to l and passes through ( 0 , − 2 ) . Slope of l line is 3. Calculation: If two lines are perpendicular, then the slope value of one line is opposite reciprocal of other line. So, the slope of the line perpendicular to l can be calculated as follows: ⊥ m = − 1 m = − 1 3 Put the given points ( 0 , − 2 ) , m in the slope intercept formula and evaluate b as follows: y = m x + b − 2 = − 1 3 ( 0 ) + b − 2 = b Thus, the y- intercept for the line perpendicular to l is − 2 . Now, substitute the value of m and b in the standard form of line equation as follows: y = m x + b y = − 1 3 x − 2 y = − 1 3 x − 2 ( 3 3 ) y = − 1 3 x − 6 3 3 y = − x − 6 x + 3 y + 6 = 0 Therefore, the standard form of line equation is x + 3 y + 6 = 0 .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 1.8, Problem 29E

To determine

To find: the standard form of line equation at given condition.

Expert Solution

Answer to Problem 29E

3x−y−2=0

Explanation of Solution

Given information:

The line equation (l) is as follows:

3x−y=10

Condition: Line is parallel to l and passes through (0,−2) .

Calculation:

Rearrange the given line equation in terms of y and compare it with the slope intercept formula as follows:

y=3x−10y=mx+b∴m=3,b=−10

If two lines are parallel, then the slope value of both the lines is same, i.e. 3

Put the given points (0,−2) in the slope intercept formula and evaluate b as follows:

y=mx+b−2=3(0)+b−2=b

Thus, the y- intercept for the line parallel to l is −2 .

Now, substitute the value of m and b in the standard form of line equation as follows:

y=mx+by=3x−23x−y−2=0

Therefore, the standard form of line equation is 3x−y−2=0 .

To determine

To find: the standard form of line equation at given condition.

Expert Solution

Answer to Problem 29E

x+3y+6=0

Explanation of Solution

Given information:

The line equation (l) is as follows:

3x−y=10

Condition: Line is perpendicular to l and passes through (0,−2) .

Slope of l line is 3.

Calculation:

If two lines are perpendicular, then the slope value of one line is opposite reciprocal of other line.

So, the slope of the line perpendicular to l can be calculated as follows:

⊥m=−1m=−13

Put the given points (0,−2) , m in the slope intercept formula and evaluate b as follows:

y=mx+b−2=−13(0)+b−2=b

Thus, the y- intercept for the line perpendicular to l is −2 .

Now, substitute the value of m and b in the standard form of line equation as follows:

y=mx+by=−13x−2y=−13x−2(33)y=−13x−633y=−x−6x+3y+6=0

Therefore, the standard form of line equation is x+3y+6=0 .

Chapter 1.8, Problem 28E

Chapter 1.8, Problem 30E

Chapter 1 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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