SOLUTION: is 9x+3y=12; 27x+9y=40 parallel, perpendicular, or neither?

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Question 748164: is 9x+3y=12; 27x+9y=40 parallel, perpendicular, or neither?
Found 2 solutions by Cromlix, tommyt3rd:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
9x + 3y = 12
3y = - 9x + 12
y = - 3x + 4 Gradient= -3
27x + 9y = 40
9y = - 27x + 40
y = - 3x + 40/9 Gradient = -3
Having the same gradients these lines are parallel

Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
We know that two lines are parallel if they have the same slope (and they are distinct). When the lines are in general form we'll use the formula m=-B/A to find their slopes with
%0D%0AAx%2BBy=C%0D%0A
%0D%0A9x%2B3y=12%0D%0A
%0D%0A27x%2B9y=40%0D%0A


first line: m=-3/9=-1/3
second line: m=-9/27=-1/3

these lines have the same slope and since we know that they are not the same line because
%0D%0A%0D%0AA%5B1%5D%2FA%5B2%5D+%3C%3E+C%5B1%5D%2FC%5B2%5D%0D%0A


they must be parallel

:)