Which equation represents a line which is parallel to the line y, equals, start fraction, 2, divided by, 3, end fraction, x, minus, 6y= 32 x−6?AnswerMultiple Choice Answers2, x, minus, 3, y, equals, 92x−3y=92, x, plus, 3, y, equals, 212x+3y=213, x, plus, 2, y, equals, minus, 103x+2y=−102, y, minus, 3, x, equals, minus, 42y−3x=−4
Question
Which equation represents a line which is parallel to the line y, equals, start fraction, 2, divided by, 3, end fraction, x, minus, 6y= 32 x−6?AnswerMultiple Choice Answers2, x, minus, 3, y, equals, 92x−3y=92, x, plus, 3, y, equals, 212x+3y=213, x, plus, 2, y, equals, minus, 103x+2y=−102, y, minus, 3, x, equals, minus, 42y−3x=−4
Solution
The question seems to be a bit jumbled, but I understand that you're asking for the equation of a line that is parallel to the line represented by the equation "y = 2/3x - 6".
Parallel lines have the same slope. The slope of the given line is 2/3. Therefore, the equation of any line parallel to the given line will be in the form "y = 2/3x + b", where "b" is the y-intercept.
Looking at the multiple choice answers:
- 2x - 3y = 9
- 2x + 3y = 21
- 3x + 2y = -10
- 2y - 3x = -4
We can rearrange these equations into slope-intercept form (y = mx + b) to find the one with a slope of 2/3.
- 3y = 2x - 9 -> y = 2/3x - 3
- 3y = 2x - 21 -> y = 2/3x - 7
- 2y = -3x - 10 -> y = -3/2x - 5
- 2y = 3x + 4 -> y = 3/2x + 2
From these, we can see that the first and second equations have a slope of 2/3, so they are parallel to the given line. The third and fourth equations are not, as their slopes are not 2/3.
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