document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218680>Question 218680</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 #164670 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=164670\">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( "(6, -2/3)\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=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 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=%28-2%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=-%288%2F3%29%2F4 ALIGN=MIDDLE  ALT=\"m=-%288%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=-8%2F12=-2%2F3 ALIGN=MIDDLE  ALT=\"m=-8%2F12=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  The slope is calculated as -2/3 or m=-2/3\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 (2,2).   Letting y=y2 and x=x2 and substituting m=-3 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 5.  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=+-2%28x-2%29%2F3=%28x-2%29%28y-2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"+-2%28x-2%29%2F3=%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=+-2%28x-2%29%2F3=y-2 ALIGN=MIDDLE  ALT=\"+-2%28x-2%29%2F3=y-2\"   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%2F3%2B4%2F3=y-2 ALIGN=MIDDLE  ALT=\"-2x%2F3%2B4%2F3=y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 2 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=-2x%2F3%2B4%2F3%2B2=y-2%2B2 ALIGN=MIDDLE  ALT=\"-2x%2F3%2B4%2F3%2B2=y-2%2B2\"   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( "<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;\" >   ANSWER in slope-intercept form.  m=-2/3 and y-intercept b=10/3\r<BR>\n" );
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document.write( "Step 7.  See if the other point (6,-2/3) or x=2 and y=0 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%2A6%2F3%2B2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3=-2%2A6%2F3%2B2%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=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So the point (6,-2/3) 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%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.\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+x+%2B+3+y+=+10 ALIGN=MIDDLE  ALT=\"2+x+%2B+3+y+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-2%2F3 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 10/2 = 5.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 10/3 = 3.33333333333333.</LI><LI>Slope is -2/3 = -0.666666666666667.</LI><LI> Equation in slope-intercept form: y=-0.666666666666667*x+3.33333333333333.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+5-8%2C+5%2B8%2C+3.33333333333333-8%2C+3.33333333333333%2B8%2C+-0.666666666666667%2Ax%2B3.33333333333333+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "And 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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document.write( "http://www.FreedomUniversity.TV </SPAN>\n" );
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