document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181883>Question 181883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients.  I am having a horrible time with these graphs, any help is greatly appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136508 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=136508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \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=-4%2Ax%2B8 ALIGN=MIDDLE  ALT=\"y=-4%2Ax%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-4 ALIGN=MIDDLE  ALT=\"m=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8 ALIGN=MIDDLE  ALT=\"b=8\"   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=-4 ALIGN=MIDDLE  ALT=\"m=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F4 ALIGN=MIDDLE  ALT=\"m=-1%2F4\"   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=1%2F4 ALIGN=MIDDLE  ALT=\"m=1%2F4\"   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=1%2F4 ALIGN=MIDDLE  ALT=\"m=1%2F4\"   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=-4 ALIGN=MIDDLE  ALT=\"m=-4\"   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\(2,-3\right\)\">.\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--3=%281%2F4%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y--3=%281%2F4%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=1%2F4 ALIGN=MIDDLE  ALT=\"m=1%2F4\"   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=-3 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-3\"   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%2B3=%281%2F4%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y%2B3=%281%2F4%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y--3 ALIGN=MIDDLE  ALT=\"y--3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3 ALIGN=MIDDLE  ALT=\"y%2B3\"   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=4%28y%2B3%29=x-2 ALIGN=MIDDLE  ALT=\"4%28y%2B3%29=x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B12=x-2 ALIGN=MIDDLE  ALT=\"4y%2B12=x-2\"   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=4y=x-2-12 ALIGN=MIDDLE  ALT=\"4y=x-2-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 12 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-x=-2-12 ALIGN=MIDDLE  ALT=\"4y-x=-2-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract \"x\" 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-x=-14 ALIGN=MIDDLE  ALT=\"4y-x=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4y=-14 ALIGN=MIDDLE  ALT=\"-x%2B4y=-14\"   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=x-4y=14 ALIGN=MIDDLE  ALT=\"x-4y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by -1 to make the \"x\" coefficient positive.\r<BR>\n" );
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document.write( "Answer: \r<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=-4%2Ax%2B8 ALIGN=MIDDLE  ALT=\"y=-4%2Ax%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through the point (2,-3) in standard form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=14 ALIGN=MIDDLE  ALT=\"x-4y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here's the graph of the two lines to verify the 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-4%2Ax%2B8%2C%2814-x%29%2F%28-4%29%29%0D%0Acircle%282%2C-3%2C0.08%29%2C%0D%0Acircle%282%2C-3%2C0.10%29%2C%0D%0Acircle%282%2C-3%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=-4%2Ax%2B8 ALIGN=MIDDLE  ALT=\"y=-4%2Ax%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and the perpendicular line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=14 ALIGN=MIDDLE  ALT=\"x-4y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(2,-3\right\)\">. <BR>\n" );
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