SOLUTION: 25. Are the following lines parallel, perpendicular, or neither? L1 with equation x � 3y = 12 L2 with equation 3x + y = 3

Question 27185: 25. Are the following lines parallel, perpendicular, or neither?
L1 with equation x � 3y = 12
L2 with equation 3x + y = 3

Answer by rodriguezh2(15) (Show Source): You can put this solution on YOUR website!
Whenever you have this type of problem you must make sure both equations are in y = mx + b form. Remember m = slope and b = (y)intercept.
L1 with equation x - 3y = 12 becomes y = (x/3) - 4
L2 with equation 3x + y = 3 becomes y = -3x +3
Parallel lines have the same slope. Therefore the m from L1 and the m from L2 must be equal. We see that (x/3) does not equal -3x so these two lines cannot be parallel.
Perpendicular lines have negative (-) reciprocal slope.
( ex: 2x and -(1/2)x.)
Since m = (x/3) from L1 and m = -3x in L2 we can say that these are negative reciprocals and so therefore these two lines are perpendicular.
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