document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82970>Question 82970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how ones like this are done?<BR>\n" );
document.write( "Graph 2x – y = 4.<BR>\n" );
document.write( "Do I need to solve this first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59546 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=59546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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;\" > 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=-y=4-2x ALIGN=MIDDLE  ALT=\"-y=4-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284-2x%29%2F-1 ALIGN=MIDDLE  ALT=\"y=%284-2x%29%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1\r<BR>\n" );
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document.write( "<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;\" > Break up the fraction and rearrange the terms so the x term is first. Now it is in <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;\" > form 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;\" > 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;\" >. So to graph this line, lets plug in point x=2 (any x value will work)\r<BR>\n" );
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document.write( "Let x=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%282%29-4 ALIGN=MIDDLE  ALT=\"y=2%282%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4-4 ALIGN=MIDDLE  ALT=\"y=4-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "So we have a point (2,0)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++grid%28+1+%29%2C%0D%0A++blue%28+circle%28+2%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+2%2C0%2C+.1%2C+1.5+%29+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here is the point (2,0) plotted on a coordinate system\r<BR>\n" );
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document.write( "Let x=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%283%29-4 ALIGN=MIDDLE  ALT=\"y=2%283%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6-4 ALIGN=MIDDLE  ALT=\"y=6-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "So we have a point (3,2). Add this to our graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++grid%28+1+%29%2C%0D%0A++blue%28+circle%28+3%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+3%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+circle%28+2%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+2%2C0%2C+.1%2C+1.5+%29+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here are the points (2,0) and (3,2) plotted on a coordinate system\r<BR>\n" );
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document.write( "Now draw a straight line through these points\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++grid%28+1+%29%2C%0D%0A++line%28-10%2C-24%2C10%2C16%29%2C%0D%0A++blue%28+circle%28+3%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+3%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+circle%28+2%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+2%2C0%2C+.1%2C+1.5+%29+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" > with the points (2,0) and (3,2)\r<BR>\n" );
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document.write( "Another way we could 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;\" > is to start with the y-intercept. We know that 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 means the y-intercept is (0,-4). So we have one point (0,-4)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++grid%28+1+%29%2C%0D%0A++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here is the point (0,-4) plotted on a coordinate system\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=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is really <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2%2F1 ALIGN=MIDDLE  ALT=\"m=2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it tells us that the next point can be found if we go 2 units up and one unit to the left to find our next point (1,-2)\r<BR>\n" );
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document.write( "So we have another point (1,-2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++grid%28+1+%29%2C%0D%0A++blue%28+circle%28+1%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+1%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Here are the points (0,-4) and (1,-2) plotted on a coordinate system\r<BR>\n" );
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document.write( "Now to make the line, just draw a straight line through the points\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++grid%28+1+%29%2C%0D%0A++line%28-10%2C-24%2C10%2C16%29%2C%0D%0A++blue%28+circle%28+1%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+1%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" > with the points (0,-4) and (1,-2)  </SPAN>\n" );
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