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Which of the following lines is parallel to the line with equation 2x+y=3?
- a)x+2y=1
- b)x-y=2
- c)3x+y=3
- d)4x+2y=6
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which of the following lines is parallel to the line with equation 2x+...
This question can be done by picking the options.
a1/a2 = b1/b2 = c1/c2
Equation : 2x + y = 3
(d) 4x + 2y = 6
a1 = 2⇒, b1 = 1, c1 = 3
a2 = 4, b2 = 2, c2 = 6
⇒ 2/4 = 1/2 = 3/6
=> 1/2 = 1/2 = 1/2
a1/a2 = b1/b2 = c1/c2
Equation : 2x + y = 3
(d) 4x + 2y = 6
a1 = 2⇒, b1 = 1, c1 = 3
a2 = 4, b2 = 2, c2 = 6
⇒ 2/4 = 1/2 = 3/6
=> 1/2 = 1/2 = 1/2
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Community Answer
Which of the following lines is parallel to the line with equation 2x+...
Analysis:
To determine which line is parallel to the given line, we need to compare the slopes of the lines. The given line has an equation of 2x - y = 3. To find the slope of this line, we can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope.
Solution:
The given line is 2x - y = 3. To rewrite it in slope-intercept form, we isolate y by subtracting 2x from both sides:
y = 2x - 3
Now we can see that the slope of the given line is 2. Any line with a slope of 2 will be parallel to the given line. Let's examine each option to find the line with a slope of 2:
Option A:
2y = 1 can be rewritten as y = 1/2, which means the slope is 1/2. This line is not parallel to the given line.
Option B:
x - y = 2 can be rewritten as y = x - 2. The slope of this line is 1, which is not equal to 2. Hence, this line is not parallel to the given line.
Option C:
3x - y = 3 can be rewritten as y = 3x - 3. The slope of this line is 3, which is not equal to 2. Therefore, this line is not parallel to the given line.
Option D:
4x - 2y = 6 can be rewritten as 2y = 4x - 6, and then further simplified as y = 2x - 3. The slope of this line is 2, which is equal to the slope of the given line. Therefore, this line is parallel to the given line.
Conclusion:
After comparing the slopes of each line, we find that only option D, 4x - 2y = 6, is parallel to the given line. Hence, option D is the correct answer.
To determine which line is parallel to the given line, we need to compare the slopes of the lines. The given line has an equation of 2x - y = 3. To find the slope of this line, we can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope.
Solution:
The given line is 2x - y = 3. To rewrite it in slope-intercept form, we isolate y by subtracting 2x from both sides:
y = 2x - 3
Now we can see that the slope of the given line is 2. Any line with a slope of 2 will be parallel to the given line. Let's examine each option to find the line with a slope of 2:
Option A:
2y = 1 can be rewritten as y = 1/2, which means the slope is 1/2. This line is not parallel to the given line.
Option B:
x - y = 2 can be rewritten as y = x - 2. The slope of this line is 1, which is not equal to 2. Hence, this line is not parallel to the given line.
Option C:
3x - y = 3 can be rewritten as y = 3x - 3. The slope of this line is 3, which is not equal to 2. Therefore, this line is not parallel to the given line.
Option D:
4x - 2y = 6 can be rewritten as 2y = 4x - 6, and then further simplified as y = 2x - 3. The slope of this line is 2, which is equal to the slope of the given line. Therefore, this line is parallel to the given line.
Conclusion:
After comparing the slopes of each line, we find that only option D, 4x - 2y = 6, is parallel to the given line. Hence, option D is the correct answer.
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