document.write( "Question 118415: Write an equation that is parrallel and perpendicular to the given line.
\n" ); document.write( "y=-1/3x+2 \n" ); document.write( "

Algebra.Com's Answer #86903 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Given line:\r
\n" ); document.write( "\n" ); document.write( " $\"y=-%281%2F3%29x%2B2\"$ ЕЕ point-slope formula where slope $\"m\"$ is $\"-1%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"Parallel\"$ lines have $\"equal+slopes\"$ ; $\"m%5B1%5D+=+m%5B2%5D\"$ . \r
\n" ); document.write( "\n" ); document.write( " $\"Perpendicular+\"$ lines have slopes whose product is $\"-1\"$ ; $\"m%5B1%5D+%2A+m%5B2%5D=+-1\"$ .\r
\n" ); document.write( "\n" ); document.write( "1) You need a line with slope $\"-1%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "So, le say that line is:\r
\n" ); document.write( "\n" ); document.write( " $\"y=-%281%2F3%29x+-+5\"$ ЕЕ point-slope formula of $\"+parallel+\"$ line\r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29x+%2B+y+=+-5\"$ ЕЕ standard formula of $\"+parallel+\"$ line\r
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\n" ); document.write( "\n" ); document.write( "here is the graph:\r
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\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: Solve the System of Equations by Graphing

\n" ); document.write( "
\n" ); document.write( " Let's look at the first equation $\"%281%2F3%29x%2By=2\"$
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\n" ); document.write( " $\"3%28%281%2F3%29x%2By%29=3%282%29\"$ Multiply both sides of the first equation by the LCD 3
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\n" ); document.write( " $\"1x%2B3y=6\"$ Distribute
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\n" ); document.write( " ---------
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\n" ); document.write( "
\n" ); document.write( " Let's look at the second equation $\"%281%2F3%29x%2By=-5\"$
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\n" ); document.write( " $\"3%28%281%2F3%29x%2By%29=3%28-5%29\"$ Multiply both sides of the second equation by the LCD 3
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\n" ); document.write( " $\"1x%2B3y=-15\"$ Distribute
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\n" ); document.write( " ---------
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\n" ); document.write( " So our new system of equations is:
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\n" ); document.write( " $\"1x%2B3y=6\"$
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\n" ); document.write( " $\"1x%2B3y=-15\"$
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\n" ); document.write( "
\n" ); document.write( " In order to graph these equations, we need to solve for y for each equation.
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\n" ); document.write( "
\n" ); document.write( " So let's solve for y on the first equation
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\n" ); document.write( " $\"1x%2B3y=6\"$ Start with the given equation
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\n" ); document.write( " $\"3y=6-x\"$ Subtract $\"+x\"$ from both sides
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\n" ); document.write( "
\n" ); document.write( " $\"3y=-x%2B6\"$ Rearrange the equation
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\n" ); document.write( " $\"y=%28-x%2B6%29%2F%283%29\"$ Divide both sides by $\"3\"$
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\n" ); document.write( " $\"y=%28-1%2F3%29x%2B%286%29%2F%283%29\"$ Break up the fraction
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\n" ); document.write( " $\"y=%28-1%2F3%29x%2B2\"$ Reduce
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\n" ); document.write( "
\n" ); document.write( " Now lets graph $\"y=%28-1%2F3%29x%2B2\"$ (note: if you need help with graphing, check out this solver)
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\n" ); document.write( "
\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%29+\"$ Graph of $\"y=%28-1%2F3%29x%2B2\"$
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\n" ); document.write( "
\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " $\"1x%2B3y=-15\"$ Start with the given equation
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\n" ); document.write( " $\"3y=-15-x\"$ Subtract $\"+x\"$ from both sides
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\n" ); document.write( "
\n" ); document.write( " $\"3y=-x-15\"$ Rearrange the equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28-x-15%29%2F%283%29\"$ Divide both sides by $\"3\"$
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\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28-1%2F3%29x%2B%28-15%29%2F%283%29\"$ Break up the fraction
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\n" ); document.write( " $\"y=%28-1%2F3%29x-5\"$ Reduce
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\n" ); document.write( "
\n" ); document.write( " Now lets add the graph of $\"y=%28-1%2F3%29x-5\"$ to our first plot to get:
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\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C%28-1%2F3%29x-5%29+\"$ Graph of $\"y=%28-1%2F3%29x%2B2\"$ (red) and $\"y=%28-1%2F3%29x-5\"$ (green)
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\n" ); document.write( " From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.

\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( "2) You need a line with slope $\"%281%2F3%29%2A+m%5B2%5D=+-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+m%5B2%5D=+-%281%2F%281%2F3%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+m%5B2%5D=+-3\"$ \r
\n" ); document.write( "\n" ); document.write( "So, le say that line is:\r
\n" ); document.write( "\n" ); document.write( " $\"y=+-3x+-+5\"$ ЕЕ point-slope formula of $\"perpendicular+\"$ line\r
\n" ); document.write( "\n" ); document.write( " $\"-3x+%2B+y+=+-5\"$ ЕЕ standard formula of $\"perpendicular+\"$ line\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "here is the graph:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: Solve the System of Equations by Graphing

\n" ); document.write( "
\n" ); document.write( " Let's look at the first equation $\"%281%2F3%29x%2By=2\"$
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"3%28%281%2F3%29x%2By%29=3%282%29\"$ Multiply both sides of the first equation by the LCD 3
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"1x%2B3y=6\"$ Distribute
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " ---------
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So our new system of equations is:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"1x%2B3y=6\"$
\n" ); document.write( "
\n" ); document.write( " $\"-3x%2By=-5\"$
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " In order to graph these equations, we need to solve for y for each equation.
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So let's solve for y on the first equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"1x%2B3y=6\"$ Start with the given equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"3y=6-x\"$ Subtract $\"+x\"$ from both sides
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"3y=-x%2B6\"$ Rearrange the equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28-x%2B6%29%2F%283%29\"$ Divide both sides by $\"3\"$
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28-1%2F3%29x%2B%286%29%2F%283%29\"$ Break up the fraction
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28-1%2F3%29x%2B2\"$ Reduce
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Now lets graph $\"y=%28-1%2F3%29x%2B2\"$ (note: if you need help with graphing, check out this solver)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%29+\"$ Graph of $\"y=%28-1%2F3%29x%2B2\"$
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So let's solve for y on the second equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"-3x%2By=-5\"$ Start with the given equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"1y=-5%2B3x\"$ Add $\"3+x\"$ to both sides
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"1y=%2B3x-5\"$ Rearrange the equation
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28%2B3x-5%29%2F%281%29\"$ Divide both sides by $\"1\"$
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=%28%2B3%2F1%29x%2B%28-5%29%2F%281%29\"$ Break up the fraction
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"y=3x-5\"$ Reduce
\n" ); document.write( "
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\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Now lets add the graph of $\"y=3x-5\"$ to our first plot to get:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C3x-5%29+\"$ Graph of $\"y=%28-1%2F3%29x%2B2\"$ (red) and $\"y=3x-5\"$ (green)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " From the graph, we can see that the two lines intersect at the point ( $\"21%2F10\"$ , $\"13%2F10\"$ ) (note: you might have to adjust the window to see the intersection)

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