document.write( "Question 923707: Find an equation of the line perpendicular to 9x+4y=6 and containing the point (1, -1). Answer in slope intercept form. Thanks for your help. \n" ); document.write( "
Algebra.Com's Answer #560259 by MathLover1(20849)\"\" \"About 
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an equation of the line perpendicular to \"9x%2B4y=6\" and containing the point (\"1\", \"-1\"):\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%289%2F4%29x%2B6%2F4\"\r
\n" ); document.write( "\n" ); document.write( "\"y=-%289%2F4%29x%2B3%2F2\" \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 \"-9%2F4\", 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%28-9%2F4%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%284%2F-9%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=4%2F9\" Multiply the fractions.
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\n" ); document.write( " So the perpendicular slope is \"4%2F9\"
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\n" ); document.write( " So now we know the slope of the unknown line is \"4%2F9\" (its the negative reciprocal of \"-9%2F4\" from the line \"y=%28-9%2F4%29%2Ax%2B3%2F2\").\n" ); document.write( "Also since the unknown line goes through (1,-1), 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%2B1=%284%2F9%29%2A%28x-1%29\" Plug in \"m=4%2F9\", \"x%5B1%5D=1\", and \"y%5B1%5D=-1\"
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\n" ); document.write( " \"y%2B1=%284%2F9%29%2Ax-%284%2F9%29%281%29\" Distribute \"4%2F9\"
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\n" ); document.write( " \"y%2B1=%284%2F9%29%2Ax-4%2F9\" Multiply
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\n" ); document.write( " \"y=%284%2F9%29%2Ax-4%2F9-1\"Subtract \"-1\" from both sides to isolate y
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\n" ); document.write( " \"y=%284%2F9%29%2Ax-4%2F9-9%2F9\" Make into equivalent fractions with equal denominators
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\n" ); document.write( " \"y=%284%2F9%29%2Ax-13%2F9\" Combine the fractions
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\n" ); document.write( " \"y=%284%2F9%29%2Ax-13%2F9\" Reduce any fractions
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\n" ); document.write( " So the equation of the line that is perpendicular to \"y=%28-9%2F4%29%2Ax%2B3%2F2\" and goes through (\"1\",\"-1\") is \"y=%284%2F9%29%2Ax-13%2F9\"
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\n" ); document.write( " So here are the graphs of the equations \"y=%28-9%2F4%29%2Ax%2B3%2F2\" and \"y=%284%2F9%29%2Ax-13%2F9\"
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\n" ); document.write( " graph of the given equation \"y=%28-9%2F4%29%2Ax%2B3%2F2\" (red) and graph of the line \"y=%284%2F9%29%2Ax-13%2F9\"(green) that is perpendicular to the given graph and goes through (\"1\",\"-1\")
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