document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105571>Question 105571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the slope of the line passing through the points (-9,3) and (4,-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76818 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the points (-9,3) and (4,-2)<BR>\n" );
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document.write( "To find the slope M of the line joining these two points you can use the formula:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"M+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you let the point {-9, 3) be the first point ... meaning its values of x and y are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+3 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... then the second point is (4, -2) which means that<BR>\n" );
document.write( "its x and y values are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+-2 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively. Then just plug these<BR>\n" );
document.write( "values into their locations in the formula and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%28-2+-+%283%29%29%2F%284+-+%28-9%29%29+=+%28-2+-3%29%2F%284%2B9%29+=+-5%2F13 ALIGN=MIDDLE  ALT=\"M+=+%28-2+-+%283%29%29%2F%284+-+%28-9%29%29+=+%28-2+-3%29%2F%284%2B9%29+=+-5%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F13 ALIGN=MIDDLE  ALT=\"-5%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You might be able to speed up the process and to do it in your head by just looking at<BR>\n" );
document.write( "the points (-9, 3) and (4, -2) and say to yourself:<BR>\n" );
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document.write( "To go from the x value of the first point to the x value of the second point, I would go<BR>\n" );
document.write( "from -9 to +4. This means that on the x-axis I would move from the left to the right 13<BR>\n" );
document.write( "numbers or +13.  At the same time, to go from the y value of the first point to the y-value<BR>\n" );
document.write( "of the second point I would go from +3 to -2 in the y-direction. Since I am moving down<BR>\n" );
document.write( "the change is negative, and the number of units to get from +3 to -2 is 5, so the change is<BR>\n" );
document.write( "-5 units.  This means the slope is -5 divided by +13 which again gives the answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F13 ALIGN=MIDDLE  ALT=\"-5%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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