document.write( "Question 111294: Are the following lines parallel, perpendicular, or neither?
\n" ); document.write( " L1 with equation x – 6y = 12
\n" ); document.write( " L2 with equation 6x + y = 6
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Algebra.Com's Answer #81163 by kmcruz09(38) $\"\"$ $\"About$

You can put this solution on YOUR website!
The line equations must first be converted to the standard form $\"y+=+mx%2Bb\"$ where m is the slope.
\n" ); document.write( "So,
\n" ); document.write( " $\"x+%96+6y+=+12\"$
\n" ); document.write( " $\"x-12=6y\"$
\n" ); document.write( " $\"y=x%2F6+-2\"$
\n" ); document.write( " $\"y=%281%2F6%29x-2\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"6x+%2B+y+=+6\"$
\n" ); document.write( " $\"y=-6x%2B6\"$ \r
\n" ); document.write( "\n" ); document.write( "Lines that are perpendicular to each other have negative reciprocal slopes, while lines that are parallel to each other have the same slopes.
\n" ); document.write( "Since we already changed the equations to the standard form, we can now take the slope.
\n" ); document.write( "For the first line, $\"y=%281%2F6%29x-2\"$ , the slope is $\"1%2F6\"$ as I said before, the literal coefficient of x is the slope in the standard form. Then for the second line, $\"y=-6x%2B6\"$ , the slope is -6.\r
\n" ); document.write( "\n" ); document.write( " $\"1%2F6\"$ and $\"-6\"$ are negative reciprocals, therefore, the two lines are perpendicular to each other.\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%281%2F6%29%2Ax+-2%2C-6x%2B6%29\"$
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