document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217337>Question 217337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the slope-intercept form of the equation of the line that passes through the given points. <BR>\n" );
document.write( "(2, 2)<BR>\n" );
document.write( "(6, -2/3)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163893 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=163893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the slope-intercept form of the equation of the line that passes through the given points. \r<BR>\n" );
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document.write( "(2, 2)<BR>\n" );
document.write( "(6, -2/3) \r<BR>\n" );
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document.write( "Step 1.  We need to find an equation in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept 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=2, x2=6 and y2=-2/3 (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 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=%28-2%2F3-2%29%2F%286-2%29 ALIGN=MIDDLE  ALT=\"m=%28-2%2F3-2%29%2F%286-2%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=%28-8%2F3%29%2F4 ALIGN=MIDDLE  ALT=\"m=%28-8%2F3%29%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%2F3 ALIGN=MIDDLE  ALT=\"m=-2%2F3\"   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=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-2%2F3 ALIGN=MIDDLE  ALT=\"m=-2%2F3\"   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 1 and choose one of the given points.  I'll choose point (2,2).   Letting y=y2 and x=x2 and substituting m=60 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%2F3=%28y-2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"+-2%2F3=%28y-2%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=+-2%2F3=%28y-2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"+-2%2F3=%28y-2%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 3(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=+-2%28x-2%29%2F3=3%28x-2%29%28y-2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"+-2%28x-2%29%2F3=3%28x-2%29%28y-2%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=+-2x%2B4=3y-6 ALIGN=MIDDLE  ALT=\"+-2x%2B4=3y-6\"   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=-2x%2B4=3y-6 ALIGN=MIDDLE  ALT=\"-2x%2B4=3y-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 6 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%2B4%2B6=3y-6%2B6 ALIGN=MIDDLE  ALT=\"-2x%2B4%2B6=3y-6%2B6\"   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%2B10=3y ALIGN=MIDDLE  ALT=\"-2x%2B10=3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by 3 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%2F3%2B10%2F3=3y%2F3 ALIGN=MIDDLE  ALT=\"-2x%2F3%2B10%2F3=3y%2F3\"   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%2F3%2B10%2F3=y ALIGN=MIDDLE  ALT=\"-2x%2F3%2B10%2F3=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "ANSWER in slope-intercept form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2F3%2B10%2F3 ALIGN=MIDDLE  ALT=\"y=-2x%2F3%2B10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where slope m=-2/3 and y-intercept=10/3\r<BR>\n" );
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document.write( "Step 8.  See if the other point (6,-2/3) or x=5 and y=-2/3 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%2F3%2B10%2F3 ALIGN=MIDDLE  ALT=\"y=-2x%2F3%2B10%2F3\"   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%2F3=-2%2F3%2A6%2B10%2F3=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3=-2%2F3%2A6%2B10%2F3=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So the other point satisfies this equation and lies on the line.\r<BR>\n" );
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document.write( "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%2B3y=10 ALIGN=MIDDLE  ALT=\"2x%2B3y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See graph below to check the above steps.  Note the slope and y-intercept as well as the x-intercept.\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-10%2C10%2C-10%2C10%2C-2x%2F3%2B10%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x%2F3%2B10%2F3%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( " <BR>\n" );
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<BR>\n" );
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