document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119657>Question 119657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x + y = 3 with no given numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87726 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you want to graph?\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=graphing_linear_equations.solver>Graphing Linear Equations</A></TD></TR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2B1%2Ay=3 ALIGN=MIDDLE  ALT=\"2%2Ax%2B1%2Ay=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ay=3-2%2Ax ALIGN=MIDDLE  ALT=\"1%2Ay=3-2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax ALIGN=MIDDLE  ALT=\"2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%29%283-2%2Ax%29 ALIGN=MIDDLE  ALT=\"y=%281%29%283-2%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <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=y=%281%29%283%29-%281%29%282%29x%29 ALIGN=MIDDLE  ALT=\"y=%281%29%283%29-%281%29%282%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <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=y=3-%282%29x ALIGN=MIDDLE  ALT=\"y=3-%282%29x\"   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=-2%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
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document.write( "  So the equation is now in slope-intercept form (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >) where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-2 ALIGN=MIDDLE  ALT=\"m=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the slope) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the y-intercept)<BR>\n" );
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document.write( "  So to graph this equation lets plug in some points<BR>\n" );
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document.write( "  Plug in x=-3<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2A%28-3%29%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2A%28-3%29%2B3\"   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=6%2B3 ALIGN=MIDDLE  ALT=\"y=6%2B3\"   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 (-3,9)<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+-13%2C8%2C+-3%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-3%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%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=-2<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2A%28-2%29%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2A%28-2%29%2B3\"   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=4%2B3 ALIGN=MIDDLE  ALT=\"y=4%2B3\"   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 (-2,7). 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+-13%2C8%2C+-3%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-2%2C7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C7%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-3%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%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+-13%2C8%2C+-3%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-13-10%2C-2%2A%28-13-10%29%2B3%2C8%2B10%2C-2%2A%288%2B10%29%2B3%29%2C%0D%0A++++blue%28+circle%28+-2%2C7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C7%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-3%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%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%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-3,9) and (-2,7)<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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) . So all of this information verifies our graph.<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=3 ALIGN=MIDDLE  ALT=\"b=3\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   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+-9%2C+13%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%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 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=3 ALIGN=MIDDLE  ALT=\"3\"   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+-9%2C+13%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+3%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+-9%2C+13%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+3%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+1%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" );
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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%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2Ax%2B3\"   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+-9%2C+13%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-2%2A%28-10-10%29%2B3%2C11%2B10%2C-2%2A%2811%2B10%29%2B3%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+3%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+1%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%2B3 ALIGN=MIDDLE  ALT=\"y=-2%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,3) and (1,1)<BR>\n" );
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