document.write( "Question 111293: 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 #81208 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First find the slope of x – 6y = 12\r
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Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)

$\"1x-6y=12\"$ Start with the given equation

$\"1x-6y-1x=12-1x\"$ Subtract 1x from both sides

$\"-6y=-1x%2B12\"$ Simplify

$\"%28-6y%29%2F%28-6%29=%28-1x%2B12%29%2F%28-6%29\"$ Divide both sides by -6 to isolate y

$\"y+=+%28-1x%29%2F%28-6%29%2B%2812%29%2F%28-6%29\"$ Break up the fraction on the right hand side

$\"y+=+%281%2F6%29x-2\"$ Reduce and simplify

The original equation $\"1x-6y=12\"$ (standard form) is equivalent to $\"y+=+%281%2F6%29x-2\"$ (slope-intercept form)

The equation $\"y+=+%281%2F6%29x-2\"$ is in the form $\"y=mx%2Bb\"$ where $\"m=1%2F6\"$ is the slope and $\"b=-2\"$ is the y intercept.

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\n" ); document.write( "\n" ); document.write( "Now find the slope of 6x + y = 6\r
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Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)

$\"6x%2B1y=6\"$ Start with the given equation

$\"6x%2B1y-6x=6-6x\"$ Subtract 6x from both sides

$\"1y=-6x%2B6\"$ Simplify

The original equation $\"6x%2B1y=6\"$ (standard form) is equivalent to $\"y+=+-6x%2B6\"$ (slope-intercept form)

The equation $\"y+=+-6x%2B6\"$ is in the form $\"y=mx%2Bb\"$ where $\"m=-6\"$ is the slope and $\"b=6\"$ is the y intercept.

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\n" ); document.write( "\n" ); document.write( "Since their product is $\"%281%2F6%29%28-6%29=-6%2F6=-1\"$ this means the two lines are perpendicular \n" ); document.write( "

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