document.write( "Question 582390: for each pair of lines given below, find out if they are parallel, perpendicular, or neither:
\n" ); document.write( "a) 5x + 2y = 6 and 3x = 2y - 12 \n" ); document.write( "

Algebra.Com's Answer #372039 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
First get the equations into the form
\n" ); document.write( " $\"+y+=+m%2Ax+%2B+b+\"$ where $\"m\"$ = slope
\n" ); document.write( " $\"+5x+%2B+2y+=+6+\"$
\n" ); document.write( " $\"+2y+=+-5x+%2B+6+\"$
\n" ); document.write( " $\"+y+=+-%285%2F2%29%2Ax+%2B+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+3x+=+2y+-+12+\"$
\n" ); document.write( " $\"+2y+=+3x+%2B+12+\"$
\n" ); document.write( " $\"+y+=+%283%2F2%29%2Ax+%2B+6+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "The slopes are different, which means
\n" ); document.write( "the lines are not parallel.
\n" ); document.write( "This also means they are not the same line.
\n" ); document.write( "-----------------
\n" ); document.write( "In order to be perpendicular, the slopes must
\n" ); document.write( "be related like this:
\n" ); document.write( " $\"+m%5B1%5D+=+-%28+1%2Fm%5B2%5D+%29+\"$
\n" ); document.write( "For these slopes, $\"+-%28+1%2F%283%2F2%29+%29+=+-%282%2F3%29+\"$ ,
\n" ); document.write( "but the other slope is $\"+-%285%2F2%29+\"$
\n" ); document.write( "so the lines are not perpendicular.
\n" ); document.write( "-----------------
\n" ); document.write( "The only choice left is that they are different lines
\n" ); document.write( "Here's a plot of the lines:
\n" ); document.write( "

\n" ); document.write( "

\n" );