document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154327>Question 154327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (-6,5);8x=5y+2<BR>\n" );
document.write( "Write an equation of the line containing the given point and the parrallel to the given line. Expess in the form y=mx+b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113632 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=113632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=5y%2B2 ALIGN=MIDDLE  ALT=\"8x=5y%2B2\"   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=8x-2=5y ALIGN=MIDDLE  ALT=\"8x-2=5y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288x-2%29%2F5=y ALIGN=MIDDLE  ALT=\"%288x-2%29%2F5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288x%29%2F5-%282%29%2F5=y ALIGN=MIDDLE  ALT=\"%288x%29%2F5-%282%29%2F5=y\"   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=%288%2F5%29x-2%2F5=y ALIGN=MIDDLE  ALT=\"%288%2F5%29x-2%2F5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So after converting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=5y%2B2 ALIGN=MIDDLE  ALT=\"8x=5y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope-intercept form, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%288%2F5%29x-2%2F5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x-2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=%288%2F5%29x-2%2F5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x-2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=8%2F5 ALIGN=MIDDLE  ALT=\"m=8%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=-2%2F5 ALIGN=MIDDLE  ALT=\"b=-2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=8%2F5 ALIGN=MIDDLE  ALT=\"m=8%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 parallel line by plugging in the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=8%2F5 ALIGN=MIDDLE  ALT=\"m=8%2F5\"   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\(-6,5\right\)\">.\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=%288%2F5%29%28x--6%29 ALIGN=MIDDLE  ALT=\"y-5=%288%2F5%29%28x--6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=8%2F5 ALIGN=MIDDLE  ALT=\"m=8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-6\"   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=%288%2F5%29%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y-5=%288%2F5%29%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x--6 ALIGN=MIDDLE  ALT=\"x--6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6 ALIGN=MIDDLE  ALT=\"x%2B6\"   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=%288%2F5%29x%2B%288%2F5%29%286%29 ALIGN=MIDDLE  ALT=\"y-5=%288%2F5%29x%2B%288%2F5%29%286%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-5=%288%2F5%29x%2B48%2F5 ALIGN=MIDDLE  ALT=\"y-5=%288%2F5%29x%2B48%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=%288%2F5%29x%2B48%2F5%2B5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x%2B48%2F5%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5 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=%288%2F5%29x%2B73%2F5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x%2B73%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 parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=5y%2B2 ALIGN=MIDDLE  ALT=\"8x=5y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-6,5\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%288%2F5%29x%2B73%2F5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x%2B73%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%288%2F5%29x-2%2F5%2C%288%2F5%29x%2B73%2F5%29%2C%0D%0Acircle%28-6%2C5%2C0.08%29%2C%0D%0Acircle%28-6%2C5%2C0.10%29%2C%0D%0Acircle%28-6%2C5%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=%288%2F5%29x-2%2F5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x-2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and the parallel line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%288%2F5%29x%2B73%2F5 ALIGN=MIDDLE  ALT=\"y=%288%2F5%29x%2B73%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(-6,5\right\)\">. <BR>\n" );
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