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Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.
- a)6x + 9y + 12 = 0
- b)9x + 12y + 36 = 0
- c)9x+ 12y- 36 = 0
- d)6x + 9y + 28 = 0
- e)6x + 9y - 28 = 0
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following line is parallel to the given line 3x + 4y = 12...
**Given Line:** 3x + 4y = 12
**Parallel Line:** A line is parallel to the given line if and only if it has the same slope.
To determine the slope of the given line, we need to rearrange the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
**Rearranging the given line:**
3x + 4y = 12
4y = -3x + 12
y = (-3/4)x + 3
**Slope:** The slope of the given line is -3/4.
Now, let's analyze the answer choices to find the line that has a negative y-intercept and the same slope as the given line.
**Answer Choices:**
a) 6x + 9y + 12 = 0
b) 9x + 12y + 36 = 0
c) 9x + 12y - 36 = 0
d) 6x + 9y + 28 = 0
e) 6x + 9y - 28 = 0
**Analyzing Each Answer Choice:**
a) 6x + 9y + 12 = 0
This equation does not have the same slope as the given line (-3/4). It is not parallel.
b) 9x + 12y + 36 = 0
This equation can be rewritten as 3x + 4y + 12 = 0. The slope is -3/4, which is the same as the given line. It also has a negative y-intercept. Therefore, this line is parallel to the given line.
c) 9x + 12y - 36 = 0
This equation can be rewritten as 3x + 4y - 12 = 0. The slope is -3/4, which is the same as the given line. However, it does not have a negative y-intercept. Therefore, this line is not parallel.
d) 6x + 9y + 28 = 0
This equation does not have the same slope as the given line (-3/4). It is not parallel.
e) 6x + 9y - 28 = 0
This equation can be rewritten as 2x + 3y - 9 = 0. The slope is -2/3, which is not the same as the given line. It is not parallel.
**Conclusion:**
The line that is parallel to the given line 3x + 4y = 12 and has a negative y-intercept is option b) 9x + 12y + 36 = 0.
**Parallel Line:** A line is parallel to the given line if and only if it has the same slope.
To determine the slope of the given line, we need to rearrange the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
**Rearranging the given line:**
3x + 4y = 12
4y = -3x + 12
y = (-3/4)x + 3
**Slope:** The slope of the given line is -3/4.
Now, let's analyze the answer choices to find the line that has a negative y-intercept and the same slope as the given line.
**Answer Choices:**
a) 6x + 9y + 12 = 0
b) 9x + 12y + 36 = 0
c) 9x + 12y - 36 = 0
d) 6x + 9y + 28 = 0
e) 6x + 9y - 28 = 0
**Analyzing Each Answer Choice:**
a) 6x + 9y + 12 = 0
This equation does not have the same slope as the given line (-3/4). It is not parallel.
b) 9x + 12y + 36 = 0
This equation can be rewritten as 3x + 4y + 12 = 0. The slope is -3/4, which is the same as the given line. It also has a negative y-intercept. Therefore, this line is parallel to the given line.
c) 9x + 12y - 36 = 0
This equation can be rewritten as 3x + 4y - 12 = 0. The slope is -3/4, which is the same as the given line. However, it does not have a negative y-intercept. Therefore, this line is not parallel.
d) 6x + 9y + 28 = 0
This equation does not have the same slope as the given line (-3/4). It is not parallel.
e) 6x + 9y - 28 = 0
This equation can be rewritten as 2x + 3y - 9 = 0. The slope is -2/3, which is not the same as the given line. It is not parallel.
**Conclusion:**
The line that is parallel to the given line 3x + 4y = 12 and has a negative y-intercept is option b) 9x + 12y + 36 = 0.
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Community Answer
Which of the following line is parallel to the given line 3x + 4y = 12...
Solution
equation is 3x+4y = 12
converting into form y=MX+c (not required can be done mentally as well)
y= -3/4 X + 12
so slope is -3/4 for a line to be parallel it must have same slope
also b and c option has that now it says negative y intercept
means y to be negative when X = 0 that is true for option b only hence the answer .
equation is 3x+4y = 12
converting into form y=MX+c (not required can be done mentally as well)
y= -3/4 X + 12
so slope is -3/4 for a line to be parallel it must have same slope
also b and c option has that now it says negative y intercept
means y to be negative when X = 0 that is true for option b only hence the answer .
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Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer?
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Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer?.
Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.a)6x + 9y + 12 = 0b)9x + 12y + 36 = 0c)9x+ 12y- 36 = 0d)6x + 9y + 28 = 0e)6x + 9y - 28 = 0Correct answer is option 'B'. Can you explain this answer?.
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