document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265318>Question 265318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graphing inequalities, I understand step one, but no further.\r<BR>\n" );
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document.write( "Example:<BR>\n" );
document.write( "3x+7y > 7 <BR>\n" );
document.write( "change to equals<BR>\n" );
document.write( "3x+7y=7<BR>\n" );
document.write( "So where do I go from here and how do I get the numbers( ?,?) to plug ion and be able to graph these questions? I hope that makes sense. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195110 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=195110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll help you graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B7y=7 ALIGN=MIDDLE  ALT=\"3x%2B7y=7\"   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=3x%2B7y=7 ALIGN=MIDDLE  ALT=\"3x%2B7y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=7-3x ALIGN=MIDDLE  ALT=\"7y=7-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=-3x%2B7 ALIGN=MIDDLE  ALT=\"7y=-3x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3x%2B7%29%2F%287%29 ALIGN=MIDDLE  ALT=\"y=%28-3x%2B7%29%2F%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-3%29%2F%287%29%29x%2B%287%29%2F%287%29 ALIGN=MIDDLE  ALT=\"y=%28%28-3%29%2F%287%29%29x%2B%287%29%2F%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F7%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%283%2F7%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F7%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%283%2F7%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the equation is 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 the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F7 ALIGN=MIDDLE  ALT=\"m=-3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is <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;\" > \r<BR>\n" );
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document.write( "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 is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\">.Remember the y-intercept is the point where the graph intersects with the y-axis\r<BR>\n" );
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document.write( "So we have one point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now since the slope is comprised of the \"rise\" over the \"run\" this means\r<BR>\n" );
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document.write( "Also, because the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F7 ALIGN=MIDDLE  ALT=\"-3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rise%2Frun=-3%2F7 ALIGN=MIDDLE  ALT=\"rise%2Frun=-3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which shows us that the rise is -3 and the run is 7. This means that to go from point to point, we can go down 3  and over 7\r<BR>\n" );
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document.write( "So starting at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\">, go down 3 units \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%28-3%2F2%29%2C2%2C-3%2C90%2C270%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and to the right 7 units to get to the next point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(7,-2\right)\">\r<BR>\n" );
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document.write( "Now draw a line through these points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F7%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%283%2F7%29x%2B1\"   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=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-%283%2F7%29x%2B1%29%2C%0D%0A++blue%28circle%280%2C1%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C1%2C.15%29%29%2C%0D%0A++blue%28circle%287%2C-2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%287%2C-2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C1%2B%28-3%2F2%29%2C2%2C-3%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%287%2F2%29%2C-2%2C7%2C2%2C+0%2C180%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=-%283%2F7%29x%2B1 ALIGN=MIDDLE  ALT=\"y=-%283%2F7%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(7,-2\right)\">\r<BR>\n" );
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document.write( "I'll leave it to you to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B7y%3E7 ALIGN=MIDDLE  ALT=\"3x%2B7y%3E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie apply the proper shading) </SPAN>\n" );
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