document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174127>Question 174127</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780132031172/algebrahomeworkh>algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find two equations with graphs that intersect at (3,-1).Show that (3,-1)<BR>\n" );
document.write( "makes both equations true. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129033 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=129033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pick two other points.  They can be anything you like, so long as they are different from (3,-1) and you don't have all three points on the same line.\r<BR>\n" );
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document.write( "(2,0) and (4,0) are convenient.\r<BR>\n" );
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document.write( "Now, find the equation of the line that passes through both (3,-1) and the first point you chose using the two-point form of the line:\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=%28%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=%28%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%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=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (3,-1) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= (2,0)\r<BR>\n" );
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document.write( "So:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=%28%280%2B1%29%2F%283-2%29%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y%2B1=%28%280%2B1%29%2F%283-2%29%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594;  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=x-3 ALIGN=MIDDLE  ALT=\"y%2B1=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594;  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-4 ALIGN=MIDDLE  ALT=\"y=x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation for the line through the points (2,0) and (3,-1).   Showing that (3,-1) makes the equation true is a simple matter of substituting 3 for x and -1 for y and showing that the result is a true statement.\r<BR>\n" );
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document.write( "Now all you need to do is select another point and use the same process shown above to create the other equation and demonstrate that (3,-1) is in the solution set.  </SPAN>\n" );
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