document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83033>Question 83033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help of the following equation: x + 3y = 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59577 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=59577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%2B3%2Ay=4 ALIGN=MIDDLE  ALT=\"1%2Ax%2B3%2Ay=4\"   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=3%2Ay=4-1%2Ax ALIGN=MIDDLE  ALT=\"3%2Ay=4-1%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax ALIGN=MIDDLE  ALT=\"1%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%2F3%29%284-1%2Ax%29 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%284-1%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" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%284%29-%281%2F3%29%281%29x%29 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%284%29-%281%2F3%29%281%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" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2F3-%281%2F3%29x ALIGN=MIDDLE  ALT=\"y=4%2F3-%281%2F3%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=%28-1%2F3%29%2Ax%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B4%2F3\"   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=%28-1%2F3%29%2Ax%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B4%2F3\"   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=-1%2F3 ALIGN=MIDDLE  ALT=\"m=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the slope) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F3 ALIGN=MIDDLE  ALT=\"b=4%2F3\"   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=%28-1%2F3%29%2A%28-8%29%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2A%28-8%29%2B4%2F3\"   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%2F3%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=8%2F3%2B4%2F3\"   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=12%2F3 ALIGN=MIDDLE  ALT=\"y=12%2F3\"   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=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  So here's one point (-8,4)<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%2C5%2C+-7%2C+14%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-8%2C4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C4%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=-5<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29%2A%28-5%29%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2A%28-5%29%2B4%2F3\"   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=5%2F3%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=5%2F3%2B4%2F3\"   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%2F3 ALIGN=MIDDLE  ALT=\"y=9%2F3\"   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=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  So here's another point (-5,3). 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%2C5%2C+-7%2C+14%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-5%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-5%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-8%2C4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C4%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%2C5%2C+-7%2C+14%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-18-10%2C-0.333333333333333%2A%28-18-10%29%2B1.33333333333333%2C5%2B10%2C-0.333333333333333%2A%285%2B10%29%2B1.33333333333333%29%2C%0D%0A++++blue%28+circle%28+-5%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-5%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-8%2C4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C4%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=%28-1%2F3%29%2Ax%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-8,4) and (-5,3)<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=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%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 -1 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=1.33333333333333 ALIGN=MIDDLE  ALT=\"1.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >) ,or (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%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=4 ALIGN=MIDDLE  ALT=\"4\"   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=4%2F3 ALIGN=MIDDLE  ALT=\"b=4%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=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   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=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   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%2C13%2C+-9.66666666666667%2C+11.3333333333333%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%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=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%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=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go down 1 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%2C13%2C+-9.66666666666667%2C+11.3333333333333%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+1.33333333333333%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 3 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%2C13%2C+-9.66666666666667%2C+11.3333333333333%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+3%2C0.333333333333333%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C0.333333333333333%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+1.33333333333333%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+0.333333333333333%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" );
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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=%28-1%2F3%29%2Ax%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B4%2F3\"   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%2C13%2C+-9.66666666666667%2C+11.3333333333333%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-0.333333333333333%2A%28-10-10%29%2B1.33333333333333%2C13%2B10%2C-0.333333333333333%2A%2813%2B10%29%2B1.33333333333333%29%2C%0D%0A++++blue%28+circle%28+3%2C0.333333333333333%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C0.333333333333333%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C1.33333333333333%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+1.33333333333333%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+0.333333333333333%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=%28-1%2F3%29%2Ax%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,1.33333333333333) and (3,0.333333333333333)<BR>\n" );
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