document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144016>Question 144016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x - 5y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104820 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=104820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you want to graph?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5y=4 ALIGN=MIDDLE  ALT=\"4x-5y=4\"   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=-5y=4-4x ALIGN=MIDDLE  ALT=\"-5y=4-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+x ALIGN=MIDDLE  ALT=\"4+x\"   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=-5y=-4x%2B4 ALIGN=MIDDLE  ALT=\"-5y=-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4x%2B4%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"y=%28-4x%2B4%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   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=y=%28-4%2F-5%29x%2B%284%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F-5%29x%2B%284%29%2F%28-5%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=%284%2F5%29x-4%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-4%2F5\"   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=%284%2F5%29x-4%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-4%2F5\"   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=4%2F5 ALIGN=MIDDLE  ALT=\"m=4%2F5\"   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%2F5 ALIGN=MIDDLE  ALT=\"b=-4%2F5\"   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%2F5 ALIGN=MIDDLE  ALT=\"b=-4%2F5\"   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,-\frac{4}{5}\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,-\frac{4}{5}\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%2F5%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%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=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   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=4%2F5 ALIGN=MIDDLE  ALT=\"rise%2Frun=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which shows us that the rise is 4 and the run is 5. This means that to go from point to point, we can go up 4  and over 5\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,-\frac{4}{5}\right)\">, go up 4 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%2F5%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C-4%2F5%2B%284%2F2%29%2C2%2C4%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 5 units to get to the next point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(5,\frac{16}{5}\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%2F5%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.15%29%29%2C%0D%0A++blue%28circle%285%2C16%2F5%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%285%2C16%2F5%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-4%2F5%2B%284%2F2%29%2C2%2C4%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%285%2F2%29%2C16%2F5%2C5%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=%284%2F5%29x-4%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-4%2F5\"   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%284%2F5%29x-4%2F5%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-4%2F5%2C.15%29%29%2C%0D%0A++blue%28circle%285%2C16%2F5%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%285%2C16%2F5%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-4%2F5%2B%284%2F2%29%2C2%2C4%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%285%2F2%29%2C16%2F5%2C5%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=%284%2F5%29x-4%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,-\frac{4}{5}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(5,\frac{16}{5}\right)\"> </SPAN>\n" );
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