document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934307>Question 934307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the equation of the line.   Perpendicular to 2x-3y+7=0 and with the same x-intercept as 4x+5y-8=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568583 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=568583\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation of the line perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%2B7=0 ALIGN=MIDDLE  ALT=\"2x-3y%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and with the same x-intercept as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y-8=0 ALIGN=MIDDLE  ALT=\"4x%2B5y-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first find x-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y-8=0 ALIGN=MIDDLE  ALT=\"4x%2B5y-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y-8=0 ALIGN=MIDDLE  ALT=\"4x%2B5y-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5%2A0-8=0 ALIGN=MIDDLE  ALT=\"4x%2B5%2A0-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=8 ALIGN=MIDDLE  ALT=\"4x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2F4 ALIGN=MIDDLE  ALT=\"x=8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the x-intercept is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "use this point and given line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%2B7=0 ALIGN=MIDDLE  ALT=\"2x-3y%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in slope intercept form to find equation of perpendicular line which passes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B7=3y ALIGN=MIDDLE  ALT=\"2x%2B7=3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x%2B7%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=equation_parallel_or_perpendicular.solver>Finding the Equation of a Line Parallel or Perpendicular to a Given Line</A></TD></TR>\n" );
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document.write( "  Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can find the perpendicular slope by this formula:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2Fm ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D ALIGN=MIDDLE  ALT=\"m%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2F%282%2F3%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So plug in the given slope to find the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=%28-1%2F1%29%283%2F2%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > When you divide fractions, you multiply the first fraction (which is really <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) by the reciprocal of the second<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-3%2F2 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fractions.<BR>\n" );
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document.write( "  So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So now we know the slope of the unknown line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its the negative reciprocal of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29%2Ax%2B7%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29%2Ax%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (2,0), we can find the equation by plugging in this info into the point-slope formula<BR>\n" );
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document.write( "  Point-Slope Formula:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where m is the slope and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is the given point<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=%28-3%2F2%29%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"y-0=%28-3%2F2%29%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F2 ALIGN=MIDDLE  ALT=\"m=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=0 ALIGN=MIDDLE  ALT=\"y%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=%28-3%2F2%29%2Ax%2B%283%2F2%29%282%29 ALIGN=MIDDLE  ALT=\"y-0=%28-3%2F2%29%2Ax%2B%283%2F2%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=%28-3%2F2%29%2Ax%2B6%2F2 ALIGN=MIDDLE  ALT=\"y-0=%28-3%2F2%29%2Ax%2B6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B6%2F2%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B6%2F2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B6%2F2%2B0%2F2 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B6%2F2%2B0%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make into equivalent fractions with equal denominators<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B6%2F2 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
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document.write( "   So the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29%2Ax%2B7%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29%2Ax%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So here are the graphs of the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29%2Ax%2B7%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29%2Ax%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-5%2C7%2C-5%2C12%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C7%2C-5%2C12%2C+0.666666666666667%2Ax%2B7%2F3%2C+-1.5%2Ax%2B3%29%2C%0D%0A+++++++++++circle%282%2C0%2C0.05%29%2C%0D%0A+++++++++++circle%282%2C0%2C0.08%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29%2Ax%2B7%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29%2Ax%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and graph of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green) that is perpendicular to the given graph and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "so, the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F2%29x%2B3 ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green) is perpendicular to line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%2B7=0 ALIGN=MIDDLE  ALT=\"2x-3y%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >(red) and has same x-intercept as a line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y-8=0 ALIGN=MIDDLE  ALT=\"4x%2B5y-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (blue )\r<BR>\n" );
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document.write( "see all three on a graph:\r<BR>\n" );
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