document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122183>Question 122183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph 2x-y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89715 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=89715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "First convert the standard equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=4 ALIGN=MIDDLE  ALT=\"2x-y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope intercept form\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=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1y=4 ALIGN=MIDDLE  ALT=\"2x-1y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1y-2x=4-2x ALIGN=MIDDLE  ALT=\"2x-1y-2x=4-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1y=-2x%2B4 ALIGN=MIDDLE  ALT=\"-1y=-2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1y%29%2F%28-1%29=%28-2x%2B4%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1y%29%2F%28-1%29=%28-2x%2B4%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate y<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2x%29%2F%28-1%29%2B%284%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2x%29%2F%28-1%29%2B%284%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the right hand side<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-4 ALIGN=MIDDLE  ALT=\"y+=+2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1y=4 ALIGN=MIDDLE  ALT=\"2x-1y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-4 ALIGN=MIDDLE  ALT=\"y+=+2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-4 ALIGN=MIDDLE  ALT=\"y+=+2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the 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 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope and <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;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-4 ALIGN=MIDDLE  ALT=\"y=2x-4\"   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=2 ALIGN=MIDDLE  ALT=\"m=2\"   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=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   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=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   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,-4\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,-4\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%2C-4%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=rise%2Frun ALIGN=MIDDLE  ALT=\"slope=rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=2 ALIGN=MIDDLE  ALT=\"2\"   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=2%2F1 ALIGN=MIDDLE  ALT=\"rise%2Frun=2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2  and over 1\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,-4\right)\">, go up 2 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%2C-4%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C-4%2B%282%2F2%29%2C2%2C2%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 1 unit to get to the next point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,-2\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%2C-4%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.15%29%29%2C%0D%0A++blue%28circle%281%2C-2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%281%2C-2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-4%2B%282%2F2%29%2C2%2C2%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%281%2F2%29%2C-2%2C1%2C2%2C+180%2C360%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\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=2x-4 ALIGN=MIDDLE  ALT=\"y=2x-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%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%2C2x-4%29%2C%0D%0A++blue%28circle%280%2C-4%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2C.15%29%29%2C%0D%0A++blue%28circle%281%2C-2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%281%2C-2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-4%2B%282%2F2%29%2C2%2C2%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%281%2F2%29%2C-2%2C1%2C2%2C+180%2C360%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=2x-4 ALIGN=MIDDLE  ALT=\"y=2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,-4\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,-2\right)\"> </SPAN>\n" );
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