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The lines represented by these equations are....

3y + 6 = 2x
and
2y - 3x = 6

The lines represented by these equations are
A) parallel
B) the same line
C) perpendicular
D) intersecting but not parallel

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Fred H. | Retired ivy league engineer math and english tutorRetired ivy league engineer math and eng...
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Put each of the equations in the slope-intercept format y = mx+b where m is the slope and b is the y-intercept. A comparison of the slopes is needed to answer the question.
Equation 1:
3y + 6 = 2x
3y = 2x - 6
y = (2/3)x - 2

Equation 2:
2y - 3x = 6
2y = 3x - 6
y = (3/2)x - 3

The slope of the first line is 2/3 and the slope of the second is 3/2

Parallel lines have slopes which are the same.
Perpendicular lines have slopes which are negative reciprocals of each other.
The two equations are different so the lines are not identical.
Lines with different slopes will intersect.

Based on this, the correct answer is D.