document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99068>Question 99068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please explain how to do this.\r<BR>\n" );
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document.write( "graph this equation<BR>\n" );
document.write( "2/3x+y/3=-1/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72084 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=72084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2/3x+y/3=-1/3<BR>\n" );
document.write( "subtract 2/3x from each side: y/3=-2/3x-1/3<BR>\n" );
document.write( "multiply 3 times each side: y=-2x-1 this is called the slope-intercept form.<BR>\n" );
document.write( "Ed<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=graphing_linear_equations.solver>Graphing Linear Equations</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=-2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we only need to plug in two points to draw the line<BR>\n" );
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document.write( "  So lets plug in some points<BR>\n" );
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document.write( "  Plug in x=-5<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2A%28-5%29-1 ALIGN=MIDDLE  ALT=\"y=-2%2A%28-5%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10-1 ALIGN=MIDDLE  ALT=\"y=10-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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document.write( "  So here's one point (-5,9)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C6%2C+-3%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-5%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-5%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now lets find another point <BR>\n" );
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document.write( "  Plug in x=-4<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2A%28-4%29-1 ALIGN=MIDDLE  ALT=\"y=-2%2A%28-4%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8-1 ALIGN=MIDDLE  ALT=\"y=8-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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document.write( "  So here's another point (-4,7). Add this to our graph<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C6%2C+-3%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-4%2C7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C7%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-5%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-5%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now draw a line through these points<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C6%2C+-3%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-15-10%2C-2%2A%28-15-10%29%2B-1%2C6%2B10%2C-2%2A%286%2B10%29%2B-1%29%2C%0D%0A++++blue%28+circle%28+-4%2C7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C7%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-5%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-5%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=-2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-5,9) and (-4,7)<BR>\n" );
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document.write( "  So from the graph we can see that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F1 ALIGN=MIDDLE  ALT=\"-2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which tells us that in order to go from point to point we have to start at one point and go  down -2 units and to the right 1 units to get to the next point), the y-intercept is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5 ALIGN=MIDDLE  ALT=\"-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) <BR>\n" );
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document.write( "  We could graph this equation another way. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1 ALIGN=MIDDLE  ALT=\"b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
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document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+-13%2C+9%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F1 ALIGN=MIDDLE  ALT=\"-2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that in order to go from point to point we can use the slope to do so. So starting at (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go down 2 units <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+-13%2C+9%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+-1%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  and to the right 1 units to get to our next point<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+-13%2C+9%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+1%2C-3%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C-3%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-1%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+-3%2C+1%2C+2%2C+0%2C+180+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Now draw a line through those points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=-2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+-13%2C+9%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-2%2A%28-10-10%29%2B-1%2C11%2B10%2C-2%2A%2811%2B10%29%2B-1%29%2C%0D%0A++++blue%28+circle%28+1%2C-3%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C-3%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-1%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+-3%2C+1%2C+2%2C+0%2C+180+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=-2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,-1) and (1,-3)<BR>\n" );
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