document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=227325>Question 227325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the slope if it exists of the lines containing the pair of points:  (2,8) and (4,-8)<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 #168966 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=168966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the slope if it exists of the lines containing the pair of points:  (2,8) and (4,-8)\r<BR>\n" );
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document.write( "Step 1.  We will put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).\r<BR>\n" );
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document.write( "Step 2.  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=2, y1=8, x2=4 and y2=-8 (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 3.  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=%28-8-8%29%2F%284-2%29 ALIGN=MIDDLE  ALT=\"m=%28-8-8%29%2F%284-2%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=-16%2F2=-8 ALIGN=MIDDLE  ALT=\"m=-16%2F2=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  The slope is calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-8 ALIGN=MIDDLE  ALT=\"m=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  Now use the slope equation of Step 2 and choose one of the given points.  I'll choose point (2,8).   Letting y=y2 and x=x2 and substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-8 ALIGN=MIDDLE  ALT=\"m=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=+-8=%28y-8%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"+-8=%28y-8%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Multiply both sides of equation by x-2 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=+-8%28x-2%29=%28x-2%29%28y-8%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"+-8%28x-2%29=%28x-2%29%28y-8%29%2F%28x-2%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=+-8%28x-2%29=y-8 ALIGN=MIDDLE  ALT=\"+-8%28x-2%29=y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7.  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=-8x%2B16=y-8 ALIGN=MIDDLE  ALT=\"-8x%2B16=y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 8 from 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=-8x%2B16%2B8=y-8%2B8 ALIGN=MIDDLE  ALT=\"-8x%2B16%2B8=y-8%2B8\"   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=-8x%2B24=y ALIGN=MIDDLE  ALT=\"-8x%2B24=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=-8x%2B24 ALIGN=MIDDLE  ALT=\"y=-8x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >   This is in slope-intercept form where the slope m=-8 and y-intercept b=+24\r<BR>\n" );
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document.write( "Step 8.  See if the other point (4,-8) or x=4 and y=-8 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=-8x%2B24 ALIGN=MIDDLE  ALT=\"y=-8x%2B24\"   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=-8=-8%2A4%2B24 ALIGN=MIDDLE  ALT=\"-8=-8%2A4%2B24\"   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=-8=-8 ALIGN=MIDDLE  ALT=\"-8=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So the point (4,-8) 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( "Step 9.  ANSWER:  The equation of the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8x%2B24 ALIGN=MIDDLE  ALT=\"y=-8x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the slope m=-8 with y-intercept b=24.\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( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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