are the lines parallel perpendicular or neither 2x+3y=-12; 2y-3x=8

Question

 2x+3y=-12; 2y-3x=8

 

Answer 1

2x+3y=-12

2y-3x=8

 

Ron G is correct that the lines are perpendicular.

He determined the slope by solving each for y

to put the equations in slope intercept form of

y = mx + b  where m is the slope and (0,b) is the

y-intercept

 

2x + 3y = -12

3y = -2x -12

y = (1/3)(-2x - 12)

y = (-2/3)x - 12/3

y = -(2/3)x -4

Slope is m=-2/3

 

2y - 3x = 8

2y = 3x + 8

y = (1/2)(3x+8)

y = (3/2)x + 4

 slope is m=3/2

 

If the slopes are negative reciprocals the lines are perpendicular.

 

-2/3 = -1/(3/2)

-2/3 = -1(2/3)

-2/3 = -2/3

Yes the slopes are negative reciprocals so the lines are perpendicular.

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You can determine the slope of a line in format ax + by = c

If you use the formula  m = -a/b.   Solving ax + by = c

gives   by = -ax + c...  y = (-a/b)x + c/b ...  Thus the slope

is  m = -a/b

 

From 2y-3x=8

         -3x + 2y = 8

        m = -a/b = -(-3)/2 = 3/2

 

From 2x + 3y = -12  

        m = -a/b = -2/3

Answer 2

OK, Abdullah: two lines are parallel if they have the same slope. That's not true here.

 

The lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. Hmmm.

 

2y - 3x = 8 has a slope of 3/2.

2x + 3y = -12 has a slope of -2/3.

 

The lines are perpendicular! Cheers!