document.write( "Question 935263: write an equation of the line that contains the
\n" ); document.write( "indicated point and meets the indicated condition(s). Write the
\n" ); document.write( "final answer in the standard form Ax + By = C, A ≥ 0.\r
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Algebra.Com's Answer #568432 by MathLover1(20850)\"\" \"About 
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\"Ax+%2B+By+=+C\", \"A+%3E=+0\".\r
\n" ); document.write( "\n" ); document.write( "(\"0\",\"-4\"); perpendicular to \"x+%2B+3y+=+9\"\r
\n" ); document.write( "\n" ); document.write( " \"3y+=-x%2B+9\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=-%281%2F3%29x%2B+3\"\r
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Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

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\n" ); document.write( " Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of \"-1%2F3\", you can find the perpendicular slope by this formula:
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\n" ); document.write( " \"m%5Bp%5D=-1%2Fm\" where \"m%5Bp%5D\" is the perpendicular slope
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\n" ); document.write( " \"m%5Bp%5D=-1%2F%28-1%2F3%29\" So plug in the given slope to find the perpendicular slope
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\n" ); document.write( " \"m%5Bp%5D=%28-1%2F1%29%283%2F-1%29\" When you divide fractions, you multiply the first fraction (which is really \"1%2F1\") by the reciprocal of the second
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\n" ); document.write( " \"m%5Bp%5D=3%2F1\" Multiply the fractions.
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\n" ); document.write( " So the perpendicular slope is \"3\"
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\n" ); document.write( " So now we know the slope of the unknown line is \"3\" (its the negative reciprocal of \"-1%2F3\" from the line \"y=%28-1%2F3%29%2Ax%2B3\").\n" ); document.write( "Also since the unknown line goes through (0,-4), we can find the equation by plugging in this info into the point-slope formula
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\n" ); document.write( " Point-Slope Formula:
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\n" ); document.write( " \"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where m is the slope and (\"x%5B1%5D\",\"y%5B1%5D\") is the given point
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\n" ); document.write( " \"y%2B4=3%2A%28x-0%29\" Plug in \"m=3\", \"x%5B1%5D=0\", and \"y%5B1%5D=-4\"
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\n" ); document.write( " \"y%2B4=3%2Ax-%283%29%280%29\" Distribute \"3\"
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\n" ); document.write( " \"y%2B4=3%2Ax-0\" Multiply
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\n" ); document.write( " \"y=3%2Ax-0-4\"Subtract \"-4\" from both sides to isolate y
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\n" ); document.write( " \"y=3%2Ax-4\" Combine like terms
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\n" ); document.write( " So the equation of the line that is perpendicular to \"y=%28-1%2F3%29%2Ax%2B3\" and goes through (\"0\",\"-4\") is \"y=3%2Ax-4\"
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\n" ); document.write( " So here are the graphs of the equations \"y=%28-1%2F3%29%2Ax%2B3\" and \"y=3%2Ax-4\"
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\n" ); document.write( " graph of the given equation \"y=%28-1%2F3%29%2Ax%2B3\" (red) and graph of the line \"y=3%2Ax-4\"(green) that is perpendicular to the given graph and goes through (\"0\",\"-4\")
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\n" ); document.write( "\n" ); document.write( "\"y+=3x-4\"in \"Ax+%2B+By+=+C\" form: \"4=3x-y\"\r
\n" ); document.write( "\n" ); document.write( "or
\n" ); document.write( "\"3x-y+=4\" where \"A=+3\"=>\"A+%3E=0\"
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