document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=376122>Question 376122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been trying for hours to solve the following type of equations and get stuck toward the end. Any help you can provide would be greatly appreciated.  The following is the problem and below is what I am trying:<BR>\n" );
document.write( "Write an equation of the line containing the given point and perpendicular to the given line <BR>\n" );
document.write( "(9, -4); 6x + 5y = 4<BR>\n" );
document.write( " ME: 5y=-6x+4<BR>\n" );
document.write( "y= 6/5x+4/5<BR>\n" );
document.write( "y-(-4)=6/5(x-9)<BR>\n" );
document.write( "I believe I have to subtract 4 from each side but this is where I keep getting confused. Thanks in advance for any help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267523 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=267523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5y=4 ALIGN=MIDDLE  ALT=\"6x%2B5y=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=5y=4-6x ALIGN=MIDDLE  ALT=\"5y=4-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   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=5y=-6x%2B4 ALIGN=MIDDLE  ALT=\"5y=-6x%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=%28-6x%2B4%29%2F%285%29 ALIGN=MIDDLE  ALT=\"y=%28-6x%2B4%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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%28-6%29%2F%285%29%29x%2B%284%29%2F%285%29 ALIGN=MIDDLE  ALT=\"y=%28%28-6%29%2F%285%29%29x%2B%284%29%2F%285%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=-%286%2F5%29x%2B4%2F5 ALIGN=MIDDLE  ALT=\"y=-%286%2F5%29x%2B4%2F5\"   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=-%286%2F5%29x%2B4%2F5 ALIGN=MIDDLE  ALT=\"y=-%286%2F5%29x%2B4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-6%2F5 ALIGN=MIDDLE  ALT=\"m=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F5 ALIGN=MIDDLE  ALT=\"b=4%2F5\"   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=-6%2F5 ALIGN=MIDDLE  ALT=\"m=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F6 ALIGN=MIDDLE  ALT=\"m=-5%2F6\"   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=5%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   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=5%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   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%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   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\(9,-4\right\)\">.\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--4=%285%2F6%29%28x-9%29 ALIGN=MIDDLE  ALT=\"y--4=%285%2F6%29%28x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=9 ALIGN=MIDDLE  ALT=\"x%5B1%5D=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-4 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-4\"   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%2B4=%285%2F6%29%28x-9%29 ALIGN=MIDDLE  ALT=\"y%2B4=%285%2F6%29%28x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y--4 ALIGN=MIDDLE  ALT=\"y--4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4 ALIGN=MIDDLE  ALT=\"y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Recall that subtracting a negative is the same as adding a positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=%285%2F6%29x%2B%285%2F6%29%28-9%29 ALIGN=MIDDLE  ALT=\"y%2B4=%285%2F6%29x%2B%285%2F6%29%28-9%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%2B4=%285%2F6%29x-15%2F2 ALIGN=MIDDLE  ALT=\"y%2B4=%285%2F6%29x-15%2F2\"   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=%285%2F6%29x-15%2F2-4 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-15%2F2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F6%29x-23%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-23%2F2\"   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=6x%2B5y=4 ALIGN=MIDDLE  ALT=\"6x%2B5y=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\(9,-4\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F6%29x-23%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-23%2F2\"   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-%286%2F5%29x%2B4%2F5%2C%285%2F6%29x-23%2F2%29%0D%0Acircle%289%2C-4%2C0.08%29%2C%0D%0Acircle%289%2C-4%2C0.10%29%2C%0D%0Acircle%289%2C-4%2C0.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Graph of the original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F5%29x%2B4%2F5 ALIGN=MIDDLE  ALT=\"y=-%286%2F5%29x%2B4%2F5\"   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=%285%2F6%29x-23%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-23%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(9,-4\right\)\">. \r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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