document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96498>Question 96498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Graph the line y=-3/2x<BR>\n" );
document.write( "2. Graph the line y=-4/3x - 4 using only slope and y intercept<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70262 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=70262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These explanations are quite long, so here is a table of contents\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=#one>Problem #1</a><BR>\n" );
document.write( "<a  rel=nofollow HREF=#two>Problem #2</a>\r<BR>\n" );
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document.write( "The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29x ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > really looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29x%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29x%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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" );
document.write( "<TR><TD  ALIGN=LEFT>In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2Ax%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > we only need to plug in two points to draw the line<BR>\n" );
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document.write( "  So lets plug in some points<BR>\n" );
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document.write( "  Plug in x=-6<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2A%28-6%29%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2A%28-6%29%2B0\"   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=18%2F2%2B0 ALIGN=MIDDLE  ALT=\"y=18%2F2%2B0\"   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=18%2F2 ALIGN=MIDDLE  ALT=\"y=18%2F2\"   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=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  So here's one point (-6,9)<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+-16%2C6%2C+-4%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-6%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%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=-4<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%2A%28-4%29%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2A%28-4%29%2B0\"   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=12%2F2%2B0 ALIGN=MIDDLE  ALT=\"y=12%2F2%2B0\"   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%2F2 ALIGN=MIDDLE  ALT=\"y=12%2F2\"   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=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  So here's another point (-4,6). 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+-16%2C6%2C+-4%2C+19%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+-6%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%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+-16%2C6%2C+-4%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-16-10%2C-1.5%2A%28-16-10%29%2B0%2C6%2B10%2C-1.5%2A%286%2B10%29%2B0%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+-6%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%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=%28-3%2F2%29%2Ax%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-6,9) and (-4,6)<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=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   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 2 units to get to the next point), the y-intercept is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) <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=0 ALIGN=MIDDLE  ALT=\"b=0\"   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=0 ALIGN=MIDDLE  ALT=\"0\"   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=0 ALIGN=MIDDLE  ALT=\"0\"   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%2C12%2C+-13%2C+10%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667-0.05%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%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   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=0 ALIGN=MIDDLE  ALT=\"0\"   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%2C12%2C+-13%2C+10%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+0%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 2 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%2C12%2C+-13%2C+10%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+2%2C-3%2C+0.146666666666667%29%29%2C%0D%0A++++blue%28+circle%28+2%2C-3%2C+0.146666666666667-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+0%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%282%2F2%29%2C+-3%2C+2%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=%28-3%2F2%29%2Ax%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B0\"   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%2C12%2C+-13%2C+10%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-1.5%2A%28-10-10%29%2B0%2C12%2B10%2C-1.5%2A%2812%2B10%29%2B0%29%2C%0D%0A++++blue%28+circle%28+2%2C-3%2C+0.146666666666667%29%29%2C%0D%0A++++blue%28+circle%28+2%2C-3%2C+0.146666666666667-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667%29%29%2C%0D%0A++++blue%28+circle%28+0%2C0%2C+0.146666666666667-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+0%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%282%2F2%29%2C+-3%2C+2%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%2F2%29%2Ax%2B0 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%2Ax%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,0) and (2,-3)<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-+4 ALIGN=MIDDLE  ALT=\"b=-+4\"   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 ALIGN=MIDDLE  ALT=\"-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<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 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=drawing%28+600%2C+600%2C+-10%2C13%2C+-18%2C+6%2C%0D%0Agrid%28+1+%29%2C%0D%0A%0D%0Ablue%28+circle%28+0%2C-4%2C+0.153333333333333%29%29%2C%0D%0Ablue%28+circle%28+0%2C-4%2C+0.153333333333333-0.05%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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%2F+3 ALIGN=MIDDLE  ALT=\"-4+%2F+3\"   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 ALIGN=MIDDLE  ALT=\"-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go down 4 units \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C+600%2C+-10%2C13%2C+-18%2C+6%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28+circle%28+0%2C-4%2C+0.153333333333333%29%29%2C%0D%0Ablue%28+circle%28+0%2C-4%2C+0.153333333333333-0.05%29+%29%0D%0Ablue%28+arc%28+0%2C+-4%2B%28-4%2F2%29%2C+2%2C+-4%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\r<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+-+4%2F3+%29+%2A+x-+4 ALIGN=MIDDLE  ALT=\"y+=+%28+-+4%2F3+%29+%2A+x-+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=drawing%28+600%2C+600%2C+-10%2C13%2C+-18%2C+6%2C%0D%0Agrid%28+1+%29%2C%0D%0Aline%28-10-10%2C-1.33333333333333%2A%28-10-10%29%2B-4%2C13%2B10%2C-1.33333333333333%2A%2813%2B10%29%2B-4%29%2C%0D%0Ablue%28+circle%28+3%2C-8%2C+0.153333333333333%29%29%2C%0D%0Ablue%28+circle%28+3%2C-8%2C+0.153333333333333-0.05+%29+%29%2C%0D%0Ablue%28+circle%28+0%2C-4%2C+0.153333333333333%29%29%2C%0D%0Ablue%28+circle%28+0%2C-4%2C+0.153333333333333-0.05%29+%29%2C%0D%0Ablue%28+arc%28+0%2C+-4%2B%28-4%2F2%29%2C+2%2C+-4%2C+90%2C+270+%29+%29%2C%0D%0Ablue%28+arc%28+%283%2F2%29%2C+-8%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+-+4%2F3+%29+%2A+x-+4 ALIGN=MIDDLE  ALT=\"y+=+%28+-+4%2F3+%29+%2A+x-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,-4) and (3,-8)\r<BR>\n" );
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