document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207553>Question 207553</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618676511/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the general form of the equation of the line that passes through (-2,-5) and is perpendicular to the graph of 3x+2y=0\r<BR>\n" );
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document.write( "Can you please show me how to figure this out? I don't even know where to begin. Thank you so very much for your help and for your time.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156947 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=156947\">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=3x%2B2y=0 ALIGN=MIDDLE  ALT=\"3x%2B2y=0\"   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=2y=-3x ALIGN=MIDDLE  ALT=\"2y=-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   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=y=%28-3x%29%2F2 ALIGN=MIDDLE  ALT=\"y=%28-3x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=-%283%2F2%29x ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\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=-%283%2F2%29x ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <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;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   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=-3%2F2 ALIGN=MIDDLE  ALT=\"m=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-2%2F3 ALIGN=MIDDLE  ALT=\"m=-2%2F3\"   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=2%2F3 ALIGN=MIDDLE  ALT=\"m=2%2F3\"   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=2%2F3 ALIGN=MIDDLE  ALT=\"m=2%2F3\"   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=-3%2F2 ALIGN=MIDDLE  ALT=\"m=-3%2F2\"   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\(-2,-5\right\)\">.\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--5=%282%2F3%29%28x--2%29 ALIGN=MIDDLE  ALT=\"y--5=%282%2F3%29%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=2%2F3 ALIGN=MIDDLE  ALT=\"m=2%2F3\"   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=-5 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-5\"   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--5=%282%2F3%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y--5=%282%2F3%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <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;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   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%2B5=%282%2F3%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y%2B5=%282%2F3%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y--5 ALIGN=MIDDLE  ALT=\"y--5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B5 ALIGN=MIDDLE  ALT=\"y%2B5\"   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%2B5=%282%2F3%29x%2B%282%2F3%29%282%29 ALIGN=MIDDLE  ALT=\"y%2B5=%282%2F3%29x%2B%282%2F3%29%282%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%2B5=%282%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y%2B5=%282%2F3%29x%2B4%2F3\"   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=%282%2F3%29x%2B4%2F3-5 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x%2B4%2F3-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 5 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=%282%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-11%2F3\"   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=3x%2B2y=0 ALIGN=MIDDLE  ALT=\"3x%2B2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-2,-5\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-11%2F3\"   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-%283%2F2%29x%2C%282%2F3%29x-11%2F3%29%0D%0Acircle%28-2%2C-5%2C0.08%29%2C%0D%0Acircle%28-2%2C-5%2C0.10%29%2C%0D%0Acircle%28-2%2C-5%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=-%283%2F2%29x ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x\"   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=%282%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-2,-5\right\)\">. <BR>\n" );
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