document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033779>Question 1033779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the angle from the line through (x,-1) and (-3,-5) to the line through (2,-5) and (4,1) is 45. find x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649058 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The line through the points (4,1) and (2,-5) has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+%281--5%29%2F%284-2%29+=+3 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+%281--5%29%2F%284-2%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, while the line through the points (-3,-5) and (x,-1) has slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D+=+%28-1--5%29%2F%28x--3%29+=+4%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"m%5B1%5D+=+%28-1--5%29%2F%28x--3%29+=+4%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the positive, acute angle between the two lines.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29+=+%28m%5B2%5D-m%5B1%5D%29%2F%281%2Bm%5B2%5D%2Am%5B1%5D%29+=+%283+-+4%2F%28x%2B3%29%29%2F%281%2B12%2F%28x%2B3%29%29 ALIGN=MIDDLE   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=tan+45%5Eo+=+1+=+%283x%2B5%29%2F%28x%2B15%29 ALIGN=MIDDLE  ALT=\"tan+45%5Eo+=+1+=+%283x%2B5%29%2F%28x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after simplification.\r<BR>\n" );
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document.write( "==> x+15 = 3x+5 ==> 10 = 2x  ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+5%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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