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Without graphing, determine whether the following pairs of lines are parallel, perpendicular, or neither 5x - 6y = 19 6x + 5y = -30

Mathematics
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So in this case: rewrite both equations so that it is easier for you to see what the slopes are. If the slopes are equal to each other, then the lines are parallel, if one slope is negative one over the slope of the other line, then these lines are perpendicular. If none of the above are true, then they are neither.
So in first case: 5x - 6y = 19 (Move 5x to the right hand side) - 6y = 19 - 5x (Multiply everything by -1) 6y = 5x - 19 (Divide everything by 6) y = (5/6)x - (19/6) <= This has the form of y = Mx+b, where M is the slope of the line. In this case the slope is: M = 5/6
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So in the second case, 6x + 5y = -30 (move 6x to the right) 5y = -30 - 6x (divide across by 5) y = -6 - (6/5)x or y = (-6/5)x - 6
In the second case, slope is -6/5 and in the first case it is 5/6. if you divide -1 by 5/6, you will get -6/5 => these lines are perpendicular
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