document.write( "Question 109407: Are the following lines parallel, perpendicular, or neither?
\n" ); document.write( " L1 with equation x – 4y = 12
\n" ); document.write( " L2 with equation 4x + y = 4
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Algebra.Com's Answer #79762 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First let's find the slope of x – 4y = 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)

$\"1x-4y=12\"$ Start with the given equation

$\"1x-4y-1x=12-1x\"$ Subtract 1x from both sides

$\"-4y=-1x%2B12\"$ Simplify

$\"%28-4y%29%2F%28-4%29=%28-1x%2B12%29%2F%28-4%29\"$ Divide both sides by -4 to isolate y

$\"y+=+%28-1x%29%2F%28-4%29%2B%2812%29%2F%28-4%29\"$ Break up the fraction on the right hand side

$\"y+=+%281%2F4%29x-3\"$ Reduce and simplify

The original equation $\"1x-4y=12\"$ (standard form) is equivalent to $\"y+=+%281%2F4%29x-3\"$ (slope-intercept form)

The equation $\"y+=+%281%2F4%29x-3\"$ is in the form $\"y=mx%2Bb\"$ where $\"m=1%2F4\"$ is the slope and $\"b=-3\"$ is the y intercept.

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\n" ); document.write( "\n" ); document.write( "Now let's find the slope of 4x + y = 4\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)

$\"4x%2B1y=4\"$ Start with the given equation

$\"4x%2B1y-4x=4-4x\"$ Subtract 4x from both sides

$\"1y=-4x%2B4\"$ Simplify

The original equation $\"4x%2B1y=4\"$ (standard form) is equivalent to $\"y+=+-4x%2B4\"$ (slope-intercept form)

The equation $\"y+=+-4x%2B4\"$ is in the form $\"y=mx%2Bb\"$ where $\"m=-4\"$ is the slope and $\"b=4\"$ is the y intercept.

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\n" ); document.write( "\n" ); document.write( "Now multiply the slopes of $\"1%2F4\"$ and $\"-4\"$ to get $\"%281%2F4%29%28-4%29=-4%2F4=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since the product of the two slopes is -1, the two slopes are perpendicular \n" ); document.write( "

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