document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198031>Question 198031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of the function f(x)=mx+b contains the points (a,2) and (-5,b) express a in terms of b, if the graph is parallel to the line 3x-9y=-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148657 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=148657\">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( "This can't be.  If you got this problem from a textbook, go ask for your money back.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = mx + b\">, then the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (0, b)\"> is guaranteed to be on the graph regardless of the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE m\">, but if the graph contains the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (-5, b)\">, then the slope of the line must be zero because:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{y_1 - y_2}{x_1 - x_2} = \frac{b - b}{0 - (-5)} = 0\">\r<BR>\n" );
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document.write( "But the slope of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x - 9y = -5\">\r<BR>\n" );
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document.write( "is found by solving for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> and taking the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y = \frac{1}{3}x + \frac{5}{9}\">\r<BR>\n" );
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document.write( "in other words, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{3}\">\r<BR>\n" );
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document.write( "Hence, the two lines cannot be parallel because:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  L_1 \parallel L_2 \ \ \Leftrightarrow\ \ m_1 = m_2\">\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 0 \neq \frac{1}{3}\">\r<BR>\n" );
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document.write( "Assuming a slope zero horizontal line, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b = 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\"> can be anything you like.\r<BR>\n" );
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document.write( "On the other hand, if the 'b' in the function definition and the 'b' in the given ordered pair are different values, which is an <b><i>unconscionably</i></b> dumb way to express this problem by the way, then you could do the problem.  So let's change the 'b' in the ordered pair to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \beta\"> so that we can avoid ambiguity.  In that case:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{y_1 - y_2}{x_1 - x_2} = \frac{2 - \beta}{a - (-5)} = \frac{1}{3}\">\r<BR>\n" );
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document.write( "and then all you need to do is solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\"> in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \beta\">\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" );
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