document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217928>Question 217928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the slope if it exists of the line containing the pair of points: \r<BR>\n" );
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document.write( "(4,5) and (8,-3)\r<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 #164211 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=164211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the slope if it exists of the line containing the pair of points: \r<BR>\n" );
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document.write( "(4,5) and (8,-3)\r<BR>\n" );
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document.write( "However, here are the steps showing you how you can check your work with one of the points.\r<BR>\n" );
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document.write( "Step 1.  The slope of the line m is given as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"+m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where for our example is x1=4, y1=5, x2=8 and y2=-3 (think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=rise%2Frun ALIGN=MIDDLE  ALT=\"slope=rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  You can choose the points the other way around but be consistent with the x and y coordinates.  You will get the same result.\r<BR>\n" );
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document.write( "Step 2.  Substituting the above values in the slope equation gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-3-5%29%2F%288-4%29 ALIGN=MIDDLE  ALT=\"m=%28-3-5%29%2F%288-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-8%2F4 ALIGN=MIDDLE  ALT=\"m=-8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-2 ALIGN=MIDDLE  ALT=\"m=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  The slope is calculated as -2 or m=-2\r<BR>\n" );
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document.write( "Step 4.  Now use the slope equation of step 1 and choose one of the given points.  I'll choose point (4,5).   Letting y=y2 and x=x2 and substituting m=-2 in the slope equation given as,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"+m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2=%28y-5%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"+-2=%28y-5%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2=%28y-5%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"+-2=%28y-5%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  Multiply both sides of equation by x-4 to get rid of denomination found on the right side of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2%28x-4%29=%28x-4%29%28y-5%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"+-2%28x-4%29=%28x-4%29%28y-5%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2%28x-4%29=y-5 ALIGN=MIDDLE  ALT=\"+-2%28x-4%29=y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Now simplify and put the above equation into slope-intercept form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B8=y-5 ALIGN=MIDDLE  ALT=\"-2x%2B8=y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 5 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B8%2B5=y-5%2B5 ALIGN=MIDDLE  ALT=\"-2x%2B8%2B5=y-5%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B13=y ALIGN=MIDDLE  ALT=\"-2x%2B13=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B13 ALIGN=MIDDLE  ALT=\"y=-2x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ANSWER in slope-intercept form.  m=-2 and y-intercept=13\r<BR>\n" );
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document.write( "Step 7.  See if the other point (8,-3) or x=8 and y=-3 satisfies this equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B13 ALIGN=MIDDLE  ALT=\"y=-2x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=-2%2A8%2B13 ALIGN=MIDDLE  ALT=\"-3=-2%2A8%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is a true statement\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=-3 ALIGN=MIDDLE  ALT=\"-3=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So the point (8,-3) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.\r<BR>\n" );
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document.write( "Note;  above equation can be also be transform into standard form as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=13 ALIGN=MIDDLE  ALT=\"2x%2By=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See graph below to check the above steps and note the slope and the y-intercept at x=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C+-5%2C15%2C-5%2C15%2C+-2x%2B13%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C+-5%2C15%2C-5%2C15%2C+-2x%2B13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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