document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206810>Question 1206810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the tables of ordered pairs represent some points on the graphs of two different lines.\r<BR>\n" );
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document.write( "Line a<BR>\n" );
document.write( "X: -11, -6, -1, 4<BR>\n" );
document.write( "Y: 81, 51, 21, -9\r<BR>\n" );
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document.write( "Line b<BR>\n" );
document.write( "X: -9, -4, 1, 6<BR>\n" );
document.write( "Y: 18, 3, -12, -27\r<BR>\n" );
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document.write( "Which systems of equations represents the graph of these two lines?<BR>\n" );
document.write( "A) x - 6y = -90, x - 3y = 27\r<BR>\n" );
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document.write( "B) x + 6y = 90, x + 3y = -27\r<BR>\n" );
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document.write( "C) 6x - y = -15, 3x - y = -9\r<BR>\n" );
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document.write( "D) 6x + y = 15, 3x + y = -9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844474 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Instead of doing all the formal algebra to find the equation of each line, let's work this problem as if we are working on a timed test, where the speed of getting the answer is important, so we want to get the answer doing as little work as possible.<br><BR>\n" );
document.write( "Here is what I would do.<br><BR>\n" );
document.write( "For the first line, the x values are -9,-4, 1, 6, a constant difference of 5; the y values are 81, 51, 21,-9, a constant difference of -30.  So the slope of the line (change in y divided by change in x) is -30/5 = -6.<br><BR>\n" );
document.write( "That makes the equation of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6x%2Bb ALIGN=MIDDLE  ALT=\"y=-6x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The answer choices all have the equations in Ax+By=C form; the equation of this line in that form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2By=b ALIGN=MIDDLE  ALT=\"6x%2By=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Only one of the answer choices (D) is in that form.  Using any one of the four given points for this line, see if that equation is correct.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2By=6%28-11%29%2B81=-66%2B81=15 ALIGN=MIDDLE  ALT=\"6x%2By=6%28-11%29%2B81=-66%2B81=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Correct!<br><BR>\n" );
document.write( "So answer choice D has the right equation for the first line; since it is the only possible correct answer, use any one of the points for line 2 to verify that the equation for line 2 in answer choice D is correct.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=3%28-9%29%2B18=-27%2B18=-9 ALIGN=MIDDLE  ALT=\"3x%2By=3%28-9%29%2B18=-27%2B18=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Correct!<br><BR>\n" );
document.write( "ANSWER: D<br><BR>\n" );
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