document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120269>Question 120269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find an equation for a line that has an unidentified slope? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88195 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=88195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First thing, do you mean 'unidentified' or 'undefined'?\r<BR>\n" );
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document.write( "If you mean 'undefined,' then you are dealing with a vertical line.  Find any point on the line and set x equal to the x-coordinate of that point.  For example, if you have a line with an undefined slope passing through the point (3,5), then the equation of the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The slope of a vertical line is undefined because if you try to compute the slope, you end up with a zero denominator.  Looking at it another way using the example here, another way to write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B0y=3 ALIGN=MIDDLE  ALT=\"x%2B0y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now if you try to put this into slope-intercept form you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B0y=3 ALIGN=MIDDLE  ALT=\"x%2B0y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0y=-x%2B3 ALIGN=MIDDLE  ALT=\"0y=-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F0%29x%2B%283%2F0%29 ALIGN=MIDDLE  ALT=\"y=-%281%2F0%29x%2B%283%2F0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > giving you an undefined slope and an undefined intercept because you are dividing by zero.\r<BR>\n" );
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document.write( "On the other hand, if you actually meant 'unidentified,' then you must know the coordinates of two points on the line.  In this case, use 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( "Just plug in the values from your two points, <b><big>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)</b></big> and <b><big>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)</b></big>.  It won't matter which point you designate 1 and which is called 2, so long as you are consistent after you have made the decision.\r<BR>\n" );
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document.write( "The reason that the two-point form works is because you are actually calculating the slope of the line with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > part.  Compare the two-point form to the point-slope form:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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