SOLUTION: for each pair of lines given below, find out if they are parallel, perpendicular, or neither: a) 5x + 2y = 6 and 3x = 2y - 12

Algebra ->  Linear-equations -> SOLUTION: for each pair of lines given below, find out if they are parallel, perpendicular, or neither: a) 5x + 2y = 6 and 3x = 2y - 12      Log On


   

Question 582390: for each pair of lines given below, find out if they are parallel, perpendicular, or neither:
a) 5x + 2y = 6 and 3x = 2y - 12
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First get the equations into the form
+y+=+m%2Ax+%2B+b+ where m = slope
+5x+%2B+2y+=+6+
+2y+=+-5x+%2B+6+
+y+=+-%285%2F2%29%2Ax+%2B+3+
and
+3x+=+2y+-+12+
+2y+=+3x+%2B+12+
+y+=+%283%2F2%29%2Ax+%2B+6+
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The slopes are different, which means
the lines are not parallel.
This also means they are not the same line.
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In order to be perpendicular, the slopes must
be related like this:
+m%5B1%5D+=+-%28+1%2Fm%5B2%5D+%29+
For these slopes, +-%28+1%2F%283%2F2%29+%29+=+-%282%2F3%29+,
but the other slope is +-%285%2F2%29+
so the lines are not perpendicular.
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The only choice left is that they are different lines
Here's a plot of the lines: