document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959328>Question 959328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do I draw x+y=11 and 2x+3y=26 onto a graph </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586589 by </B><A HREF=/tutors/aboutme.mpl?userid=EdenWolf><B>EdenWolf(517)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EdenWolf><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=EdenWolf><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)<TABLE  BORDER=1>\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=-1%2Ax%2B11 ALIGN=MIDDLE  ALT=\"y=-1%2Ax%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > we only need to plug in two points to draw the line<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets plug in some points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2A%282%29%2B11 ALIGN=MIDDLE  ALT=\"y=-1%2A%282%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2B11 ALIGN=MIDDLE  ALT=\"y=-2%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  So here's one point (2,9)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-8%2C13%2C+-2%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+2%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets find another point <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=3<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2A%283%29%2B11 ALIGN=MIDDLE  ALT=\"y=-1%2A%283%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2B11 ALIGN=MIDDLE  ALT=\"y=-3%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's another point (3,8). Add this to our graph<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-8%2C13%2C+-2%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+3%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+2%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now draw a line through these points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-8%2C13%2C+-2%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-8-10%2C-1%2A%28-8-10%29%2B11%2C13%2B10%2C-1%2A%2813%2B10%29%2B11%29%2C%0D%0A++++blue%28+circle%28+3%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+2%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%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=-1%2Ax%2B11 ALIGN=MIDDLE  ALT=\"y=-1%2Ax%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (2,9) and (3,8)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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=-1%2F1 ALIGN=MIDDLE  ALT=\"-1%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 -1 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=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >)and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  We could graph this equation another way. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=11 ALIGN=MIDDLE  ALT=\"b=11\"   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=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+0%2C+21%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14-0.05%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F1 ALIGN=MIDDLE  ALT=\"-1%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=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go down 1 units <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+0%2C+21%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+11%2B%28-1%2F2%29%2C+2%2C+-1%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" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+0%2C+21%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+1%2C10%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C10%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+11%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+10%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=-1%2Ax%2B11 ALIGN=MIDDLE  ALT=\"y=-1%2Ax%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+0%2C+21%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-1%2A%28-10-10%29%2B11%2C11%2B10%2C-1%2A%2811%2B10%29%2B11%29%2C%0D%0A++++blue%28+circle%28+1%2C10%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C10%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C11%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+11%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+10%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=-1%2Ax%2B11 ALIGN=MIDDLE  ALT=\"y=-1%2Ax%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,11) and (1,10)<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "2)<TABLE  BORDER=1>\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><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2B3%2Ay=26 ALIGN=MIDDLE  ALT=\"2%2Ax%2B3%2Ay=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given equation<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ay=26-2%2Ax ALIGN=MIDDLE  ALT=\"3%2Ay=26-2%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" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2826-2%2Ax%29 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2826-2%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%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2826%29-%281%2F3%29%282%29x%29 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2826%29-%281%2F3%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%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=26%2F3-%282%2F3%29x ALIGN=MIDDLE  ALT=\"y=26%2F3-%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29%2Ax%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2Ax%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29%2Ax%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2Ax%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
document.write( "  <BR>\n" );
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%2F3 ALIGN=MIDDLE  ALT=\"m=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the slope) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=26%2F3 ALIGN=MIDDLE  ALT=\"b=26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the y-intercept)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So to graph this equation lets plug in some points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=1<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29%2A%281%29%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2A%281%29%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2F3%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=-2%2F3%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24%2F3 ALIGN=MIDDLE  ALT=\"y=24%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's one point (1,8)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-9%2C14%2C+-4%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+1%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets find another point <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=4<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%2F3%29%2A%284%29%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2A%284%29%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8%2F3%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=-8%2F3%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=18%2F3 ALIGN=MIDDLE  ALT=\"y=18%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's another point (4,6). Add this to our graph<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-9%2C14%2C+-4%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+4%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+4%2C6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+1%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now draw a line through these points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-9%2C14%2C+-4%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-9-10%2C-0.666666666666667%2A%28-9-10%29%2B8.66666666666667%2C14%2B10%2C-0.666666666666667%2A%2814%2B10%29%2B8.66666666666667%29%2C%0D%0A++++blue%28+circle%28+4%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+4%2C6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+1%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C8%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=%28-2%2F3%29%2Ax%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2Ax%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (1,8) and (4,6)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   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 3 units to get to the next point), the y-intercept is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.66666666666667 ALIGN=MIDDLE  ALT=\"8.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >) ,or (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2F3 ALIGN=MIDDLE  ALT=\"26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) . So all of this information verifies our graph.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  We could graph this equation another way. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=26%2F3 ALIGN=MIDDLE  ALT=\"b=26%2F3\"   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=26%2F3 ALIGN=MIDDLE  ALT=\"26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2F3 ALIGN=MIDDLE  ALT=\"26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C13%2C+-3.33333333333333%2C+18.6666666666667%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now since the slope is <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;\" >, 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=26%2F3 ALIGN=MIDDLE  ALT=\"26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go down 2 units <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C13%2C+-3.33333333333333%2C+18.6666666666667%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+8.66666666666667%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 3 units to get to our next point<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C13%2C+-3.33333333333333%2C+18.6666666666667%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+3%2C6.66666666666667%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C6.66666666666667%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+8.66666666666667%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+6.66666666666667%2C+3%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( "  <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=%28-2%2F3%29%2Ax%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2Ax%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C13%2C+-3.33333333333333%2C+18.6666666666667%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-0.666666666666667%2A%28-10-10%29%2B8.66666666666667%2C13%2B10%2C-0.666666666666667%2A%2813%2B10%29%2B8.66666666666667%29%2C%0D%0A++++blue%28+circle%28+3%2C6.66666666666667%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C6.66666666666667%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8.66666666666667%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+8.66666666666667%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+6.66666666666667%2C+3%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=%28-2%2F3%29%2Ax%2B26%2F3 ALIGN=MIDDLE  ALT=\"y=%28-2%2F3%29%2Ax%2B26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,8.66666666666667) and (3,6.66666666666667)<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );