document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173085>Question 173085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the slope-intercept form of the equation of the line that is perpendicular to 5x + 4y + 4  and contains (-1, 9). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127920 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is the equation supposed to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+4y+=+4 ALIGN=MIDDLE  ALT=\"5x+%2B+4y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I'll assume that it is.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B4y=4 ALIGN=MIDDLE  ALT=\"5x%2B4y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=4-5x ALIGN=MIDDLE  ALT=\"4y=4-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-5x%2B4 ALIGN=MIDDLE  ALT=\"4y=-5x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5x%2B4%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y=%28-5x%2B4%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-5%29%2F%284%29%29x%2B%284%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y=%28%28-5%29%2F%284%29%29x%2B%284%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F4%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%285%2F4%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "We can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F4%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%285%2F4%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F4 ALIGN=MIDDLE  ALT=\"m=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now to find the slope of the perpendicular line, simply flip the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F4 ALIGN=MIDDLE  ALT=\"m=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-4%2F5 ALIGN=MIDDLE  ALT=\"m=-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now change the sign to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4%2F5 ALIGN=MIDDLE  ALT=\"m=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4%2F5 ALIGN=MIDDLE  ALT=\"m=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F4 ALIGN=MIDDLE  ALT=\"m=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the coordinates of the given point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-1,9\right\)\">.\r<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;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-9=%284%2F5%29%28x--1%29 ALIGN=MIDDLE  ALT=\"y-9=%284%2F5%29%28x--1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4%2F5 ALIGN=MIDDLE  ALT=\"m=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=9 ALIGN=MIDDLE  ALT=\"y%5B1%5D=9\"   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-9=%284%2F5%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"y-9=%284%2F5%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x--1 ALIGN=MIDDLE  ALT=\"x--1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   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-9=%284%2F5%29x%2B%284%2F5%29%281%29 ALIGN=MIDDLE  ALT=\"y-9=%284%2F5%29x%2B%284%2F5%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-9=%284%2F5%29x%2B4%2F5 ALIGN=MIDDLE  ALT=\"y-9=%284%2F5%29x%2B4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F5%29x%2B4%2F5%2B9 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x%2B4%2F5%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 9 to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F5%29x%2B49%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x%2B49%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. note: If you need help with fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a>.\r<BR>\n" );
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document.write( "So the equation of the line perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B4y=4 ALIGN=MIDDLE  ALT=\"5x%2B4y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-1,9\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F5%29x%2B49%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x%2B49%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here's a graph to visually verify our answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%285%2F4%29x%2B1%2C%284%2F5%29x%2B49%2F5%29%0D%0Acircle%28-1%2C9%2C0.08%29%2C%0D%0Acircle%28-1%2C9%2C0.10%29%2C%0D%0Acircle%28-1%2C9%2C0.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Graph of the original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F4%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%285%2F4%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and the perpendicular line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F5%29x%2B49%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x%2B49%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-1,9\right\)\">. <BR>\n" );
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