document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=390709>Question 390709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help graphing y + 5 = -3/4 (x-6).     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277080 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=277080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+5+=+-3%2F4+%28x-6%29 ALIGN=MIDDLE  ALT=\"y+%2B+5+=+-3%2F4+%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=4y+%2B+5%2A4+=+-%283x%2F4%294+-6%2A4%29 ALIGN=MIDDLE  ALT=\"4y+%2B+5%2A4+=+-%283x%2F4%294+-6%2A4%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=4y+%2B+20+=+-3x+-24%29 ALIGN=MIDDLE  ALT=\"4y+%2B+20+=+-3x+-24%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=4y+=+-3x+-24+-20%29 ALIGN=MIDDLE  ALT=\"4y+=+-3x+-24+-20%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=4y+=+-3x+-44+%29 ALIGN=MIDDLE  ALT=\"4y+=+-3x+-44+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "standard form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B4y+=+-+44+%29 ALIGN=MIDDLE  ALT=\"3x+%2B4y+=+-+44+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "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( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2B4%2Ay=-44 ALIGN=MIDDLE  ALT=\"3%2Ax%2B4%2Ay=-44\"   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=4%2Ay=-44-3%2Ax ALIGN=MIDDLE  ALT=\"4%2Ay=-44-3%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax ALIGN=MIDDLE  ALT=\"3%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%2F4%29%28-44-3%2Ax%29 ALIGN=MIDDLE  ALT=\"y=%281%2F4%29%28-44-3%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%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   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%2F4%29%28-44%29-%281%2F4%29%283%29x%29 ALIGN=MIDDLE  ALT=\"y=%281%2F4%29%28-44%29-%281%2F4%29%283%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   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=-44%2F4-%283%2F4%29x ALIGN=MIDDLE  ALT=\"y=-44%2F4-%283%2F4%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=%28-3%2F4%29%2Ax-44%2F4 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2Ax-44%2F4\"   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=%28-3%2F4%29%2Ax-11 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2Ax-11\"   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=-3%2F4 ALIGN=MIDDLE  ALT=\"m=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the slope) and <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;\" > (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=-8<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F4%29%2A%28-8%29-11 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2A%28-8%29-11\"   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=24%2F4-11 ALIGN=MIDDLE  ALT=\"y=24%2F4-11\"   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=-20%2F4 ALIGN=MIDDLE  ALT=\"y=-20%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  So here's one point (-8,-5)<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+-18%2C6%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-8%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C-5%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=%28-3%2F4%29%2A%28-4%29-11 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2A%28-4%29-11\"   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=12%2F4-11 ALIGN=MIDDLE  ALT=\"y=12%2F4-11\"   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=-32%2F4 ALIGN=MIDDLE  ALT=\"y=-32%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
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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" );
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document.write( "  So here's another point (-4,-8). 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+-18%2C6%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-4%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C-8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-8%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C-5%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+-18%2C6%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-18-10%2C-0.75%2A%28-18-10%29%2B-11%2C6%2B10%2C-0.75%2A%286%2B10%29%2B-11%29%2C%0D%0A++++blue%28+circle%28+-4%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C-8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-8%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C-5%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=%28-3%2F4%29%2Ax-11 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2Ax-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-8,-5) and (-4,-8)<BR>\n" );
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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=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   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 -3 units and to the right 4 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=-14.6666666666667 ALIGN=MIDDLE  ALT=\"-14.6666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-44%2F3 ALIGN=MIDDLE  ALT=\"-44%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) . So all of this information verifies our graph.<BR>\n" );
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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" );
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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" );
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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%2C14%2C+-24%2C+-1%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-11%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%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=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   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 3 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%2C14%2C+-24%2C+-1%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-11%2B%28-3%2F2%29%2C+2%2C+-3%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 4 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%2C14%2C+-24%2C+-1%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+4%2C-14%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+4%2C-14%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-11%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%284%2F2%29%2C+-14%2C+4%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=%28-3%2F4%29%2Ax-11 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2Ax-11\"   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%2C14%2C+-24%2C+-1%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-0.75%2A%28-10-10%29%2B-11%2C14%2B10%2C-0.75%2A%2814%2B10%29%2B-11%29%2C%0D%0A++++blue%28+circle%28+4%2C-14%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+4%2C-14%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-11%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-11%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%284%2F2%29%2C+-14%2C+4%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=%28-3%2F4%29%2Ax-11 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29%2Ax-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,-11) and (4,-14)<BR>\n" );
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