document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375101>Question 375101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I may have this one figured out. I will show you what I have so far. The question is Determine whether the graphs of each pair of lines are parallel. \r<BR>\n" );
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document.write( "2x+4 = y and\r<BR>\n" );
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document.write( "2y = 4x - 7. \r<BR>\n" );
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document.write( "I worked them out as the first line being 2 for the slope and the second being -7/2. I think these lines are NOT parallel because the slopes are different for each. <BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266739 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Given the values you determined for the slope, you came to the correct conclusion.  Whenever the slopes are NOT equal, the lines are NOT parallel.  Unfortunately, you made an error when calculating the slope for the second equation.  The slope for the first equation is indeed 2 as a simple swap of sides shows us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 2x\ +\ 4\">\r<BR>\n" );
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document.write( "And we can see that with the equation in slope-intercept form, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ mx\ +\ b\">, that the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, and therefore the slope, is 2.\r<BR>\n" );
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document.write( "But if you solve the other equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> by dividing both sides by 2, you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 2x\ -\ \frac{7}{2}\">\r<BR>\n" );
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document.write( "And the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is again 2, so the slope of the second line is also 2.  What is different is the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-intercept, that is, the constant term.  This tells us that even though the two lines have the same slope, the place they intersect the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-axis is different.  Hence, these two lines are indeed parallel (as opposed to being the same line)\r<BR>\n" );
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document.write( "See?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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