document.write( "Question 580809: Determine whether the lines are parallel,perpendicular,neither,unknown or impossible to say.7x+2y=14;7y=2x-5
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Algebra.Com's Answer #371662 by KMST(5328) $\"\"$ $\"About$

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We have to look at the slopes, if they exist.
\n" ); document.write( "Subtracting 7x from both sides of the equal sign in $\"7x%2B2y=14\"$ , and then dividing both sides by 2, we get to the slope-intercept form of the equation:
\n" ); document.write( " $\"7x%2B2y=14\"$ --> $\"2y=-7x%2B14\"$ --> $\"y=%28-7%2F2%29x%2B2\"$
\n" ); document.write( "The slope is $\"-7%2F2\"$ , the coefficient of the $\"x\"$ .
\n" ); document.write( "It's even easier for the other equation. Just divide both sides by 7.
\n" ); document.write( " $\"7y=2x-5\"$ --> $\"y=%282%2F7%29x-5%2F7\"$
\n" ); document.write( "The slope is $\"2%2F7\"$ .
\n" ); document.write( "The lines these equations represent would be parallel if and only if the slopes were the same. So these lines are not parallel.
\n" ); document.write( "The lines would be perpendicular if the product of the slopes were -1. Let's multiply:
\n" ); document.write( " $\"%28-7%2F2%29%282%2F7%29=-7%2A2%2F%282%2A7%29=-1\"$ The lines are $\"highlight+%28perpendicular%29\"$ .
\n" ); document.write( "If the slopes were different, and the product was something other than -1, the lines would be neither. Once we find the slopes, unknown is not an option.
\n" ); document.write( "Horizontal lines, with equations equivalent to $\"y=some\"$ $\"number\"$ , have $\"slope=0\"$ .
\n" ); document.write( "The only lines that have no slope are vertical lines, whose equations are equivalent to $\"x=some\"$ $\"number\"$ . Vertical lines are parallel to other vertical lines, and perpendicular to horizontal lines. Vertical lines are neither parallel nor perpendicular to lines with non-zero slope. \n" ); document.write( "

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