document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217410>Question 217410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation in slope-intercept form that passes through (4, 9) and (5, 12) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163944 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=163944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation in slope-intercept form that passes through (4, 9) and (5, 12)\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=4, y1=9, x2=5 and y2=12 (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=%2812-9%29%2F%285-4%29 ALIGN=MIDDLE  ALT=\"m=%2812-9%29%2F%285-4%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=3%2F1=3 ALIGN=MIDDLE  ALT=\"m=3%2F1=3\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   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 (4,9).   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=+3=%28y-9%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"+3=%28y-9%29%2F%28x-4%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-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=+3%28x-4%29=%28x-4%29%28y-9%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"+3%28x-4%29=%28x-4%29%28y-9%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=+3x-12=%28y-9%29 ALIGN=MIDDLE  ALT=\"+3x-12=%28y-9%29\"   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=3x-12=y-9 ALIGN=MIDDLE  ALT=\"3x-12=y-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 9 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=3x-12%2B9=y-9%2B9 ALIGN=MIDDLE  ALT=\"3x-12%2B9=y-9%2B9\"   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=3x-3=y ALIGN=MIDDLE  ALT=\"3x-3=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=3x-3 ALIGN=MIDDLE  ALT=\"y=3x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where slope m=3 band y-intercept=-3\r<BR>\n" );
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document.write( "Step 8.  See if the other point (5,12) or x=5 and y=12 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=3x-3 ALIGN=MIDDLE  ALT=\"y=3x-3\"   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=12=3%2A5-3=12 ALIGN=MIDDLE  ALT=\"12=3%2A5-3=12\"   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=3x-y=3 ALIGN=MIDDLE  ALT=\"3x-y=3\"   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%28600%2C600%2C-15%2C15%2C-10%2C10%2C3x-3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-15%2C15%2C-10%2C10%2C3x-3%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<BR>\n" );
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