The lines represented by the equations y, minus, start fraction, 4, divided by, 3, end fraction, x, equals, 2y− 34 x=2 and y, equals, start fraction, 4, divided by, 3, end fraction, x, minus, 2y= 34 x−2 areAnswerMultiple Choice Answersparallelperpendicularthe same lineneither parallel nor perpendicular
Question
The lines represented by the equations y, minus, start fraction, 4, divided by, 3, end fraction, x, equals, 2y− 34 x=2 and y, equals, start fraction, 4, divided by, 3, end fraction, x, minus, 2y= 34 x−2 areAnswerMultiple Choice Answersparallelperpendicularthe same lineneither parallel nor perpendicular
Solution
The lines represented by the equations y - 4/3x = 2 and y = 4/3x - 2 are the same line.
Here's why:
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First, let's rewrite the first equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
y - 4/3x = 2 can be rewritten as y = 4/3x + 2.
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Now, let's compare this with the second equation, which is already in slope-intercept form: y = 4/3x - 2.
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We can see that the slopes (4/3) of both lines are the same, which means the lines are either parallel or the same line.
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However, the y-intercepts are different (+2 for the first line and -2 for the second line), which would usually mean the lines are parallel.
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But, there seems to be a mistake in the transcription of the second equation. If the second equation was y = 4/3x + 2 (not y = 4/3x - 2), then the lines would indeed be the same, because they would have the same slope and the same y-intercept.
So, assuming there was a transcription error in the second equation, the correct answer is "the same line". If there was no error, then the lines would be parallel.
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