document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187172>Question 187172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line containing the point (-2,-5) and parallel to the line 4x-5y=13.<BR>\n" );
document.write( "I tried to solve the above problem and came up with the following answer:<BR>\n" );
document.write( "-5y/5=-4x/5+13/5.... y=-4/5x+13/5 ...(slope=-4/5.  The answer is supposed to be y=-4/5x+17/5.  I don't understand where 17 came from.\r<BR>\n" );
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document.write( "Thank you for your help with this problem.<BR>\n" );
document.write( "Judy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140293 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=140293\">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=4x-5y=13 ALIGN=MIDDLE  ALT=\"4x-5y=13\"   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=13-4x ALIGN=MIDDLE  ALT=\"-5y=13-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   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=-4x%2B13 ALIGN=MIDDLE  ALT=\"-5y=-4x%2B13\"   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=%28-4x%2B13%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"y=%28-4x%2B13%29%2F%28-5%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%28-4%29%2F%28-5%29%29x%2B%2813%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"y=%28%28-4%29%2F%28-5%29%29x%2B%2813%29%2F%28-5%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=%284%2F5%29x-13%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-13%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=%284%2F5%29x-13%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-13%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <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;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-13%2F5 ALIGN=MIDDLE  ALT=\"b=-13%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=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 parallel line by plugging in the slope <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;\" >  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=%284%2F5%29%28x--2%29 ALIGN=MIDDLE  ALT=\"y--5=%284%2F5%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=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=-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=%284%2F5%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y--5=%284%2F5%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=%284%2F5%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y%2B5=%284%2F5%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=%284%2F5%29x%2B%284%2F5%29%282%29 ALIGN=MIDDLE  ALT=\"y%2B5=%284%2F5%29x%2B%284%2F5%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=%284%2F5%29x%2B8%2F5 ALIGN=MIDDLE  ALT=\"y%2B5=%284%2F5%29x%2B8%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%2B8%2F5-5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x%2B8%2F5-5\"   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=%284%2F5%29x-17%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \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=4x-5y=13 ALIGN=MIDDLE  ALT=\"4x-5y=13\"   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=%284%2F5%29x-17%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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