document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104173>Question 1104173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the slope of the line that passes through the point (2,6) and the point (7,-7)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718909 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=718909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Formally, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"slope+=+%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For the given points, that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7-6%29%2F%287-2%29+=+-13%2F5 ALIGN=MIDDLE  ALT=\"%28-7-6%29%2F%287-2%29+=+-13%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "But I encourage you not to just plug numbers into the magic formula and move on to the next problem without checking to see if your answer makes sense.  It is far too easy to get the wrong numbers in the wrong place if you just use the formula without thinking.<br><BR>\n" );
document.write( "Think of what slope means in the real world.  You are hiking in the mountains; slope tells you how far you move up or down for each step forward.  So think of walking from left to right from one point to the other.  How far do you move forward (difference in x values), and how far do you move up or down (difference in y values?<br><BR>\n" );
document.write( "When I see these two points and need to find the slope, I first see that the first point (2,6) is to the left of the second (7,-7).  So I'm walking from the first point to the second.  How far do I move forward?  From 2 to 7, a distance of 5.  In that time, how far do I move up or down?  From 6 to -7, a change of -13.  So my slope is -13/5.<br><BR>\n" );
document.write( "If you do something like that to calculate the slope between two points, you will have a better understanding of the mathematics; and you will make fewer mistakes.<br><BR>\n" );
document.write( "And if you choose to simply use the slope formula to find the slope, then at least take a moment to see if your answer is reasonable.  With the given points, if you make an arithmetic error and get a slope of 7 or -1/4, a quick sketch of the two points -- in your head, or with pencil and paper -- will tell you that you made an arithmetic error somewhere. </SPAN>\n" );
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