document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329030>Question 329030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q) Find the angle &#952; (in radians and degrees) between the lines. Round to three decimal places, if necessary.<BR>\n" );
document.write( "6x + 2y = 9<BR>\n" );
document.write( "–5x + 6y = 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235836 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The angle that the line makes with respect to the y axis has a relationship to the line. <BR>\n" );
document.write( "The tangent of the angle is equal to the change in y divided by the change in x using trigonmetry. <BR>\n" );
document.write( "But the change in y over the change in x is also the slope of the line. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=tan%28theta%29 ALIGN=MIDDLE  ALT=\"m=tan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Convert both lines to slope intercept form and find their slopes. <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B+2y+=+9 ALIGN=MIDDLE  ALT=\"6x+%2B+2y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-6x%2B9 ALIGN=MIDDLE  ALT=\"2y=-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B9%2F2 ALIGN=MIDDLE  ALT=\"y=-3x%2B9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1=tan%28alpha%29=-3 ALIGN=MIDDLE  ALT=\"m1=tan%28alpha%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=1.893 ALIGN=MIDDLE  ALT=\"alpha=1.893\"   DISABLED_style= \"max-width:90%; height:auto;\" >radians<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x+%2B+6y+=+4 ALIGN=MIDDLE  ALT=\"-5x+%2B+6y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=5x%2B4 ALIGN=MIDDLE  ALT=\"6y=5x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F6%29x%2B2%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=tan%28beta%29=5%2F6 ALIGN=MIDDLE  ALT=\"m2=tan%28beta%29=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta=0.695 ALIGN=MIDDLE  ALT=\"beta=0.695\"   DISABLED_style= \"max-width:90%; height:auto;\" >radians<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "The angle between them <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > is then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=1.893-0.695=1.199 ALIGN=MIDDLE  ALT=\"X=1.893-0.695=1.199\"   DISABLED_style= \"max-width:90%; height:auto;\" >radians<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=1.199%28360%2F2pi%29=68.629 ALIGN=MIDDLE  ALT=\"X=1.199%28360%2F2pi%29=68.629\"   DISABLED_style= \"max-width:90%; height:auto;\" >degrees<BR>\n" );
document.write( ".<BR>\n" );
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document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Clocate%281%2C3%2CX%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-3x%2B9%2F2%2C%285%2F6%29x%2B2%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );