document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78912>Question 78912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the slope and the y-intercept.\r<BR>\n" );
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document.write( "x = -9<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56587 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=56587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This one checks your understanding of graphing.<BR>\n" );
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document.write( "The graph of x = -9 is a vertical line through the point -9 on the x-axis.<BR>\n" );
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document.write( "You can interpret this line as meaning that the value of x is always -9 for any point<BR>\n" );
document.write( "on the graph.<BR>\n" );
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document.write( "The slope of a vertical line is undefined. Note that undefined is not the same as zero.<BR>\n" );
document.write( "A line with zero slope is a horizontal line.<BR>\n" );
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document.write( "Recall that the equation for slope is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"slope+=+%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( "But for the equation you were given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=+-9 ALIGN=MIDDLE  ALT=\"x%5B2%5D=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" > because x is always<BR>\n" );
document.write( "the same value.  Therefore, the equation for the slope becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28-9+-%28-9%29%29 ALIGN=MIDDLE  ALT=\"slope+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28-9+-%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and if you simplify the denominator by combining terms, it becomes 0.  But in algebra<BR>\n" );
document.write( "division by zero is not permitted.  Therefore, the slope of the vertical line is classified<BR>\n" );
document.write( "as undefined.<BR>\n" );
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document.write( "Notice also that since the graph of x = -9 is a vertical line, it is parallel to the y-axis.<BR>\n" );
document.write( "And from geometry ... parallel lines never intersect.  Therefore, the graph never <BR>\n" );
document.write( "intersects the y-axis.  <BR>\n" );
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document.write( "Hope this helps you to understand the characteristics of the graphs when you have an<BR>\n" );
document.write( "equation that defines x as being equal to some constant.  The graph will be vertical,<BR>\n" );
document.write( "will have an undefined slope, and will not intersect the y-axis.<BR>\n" );
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