document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153545>Question 153545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the following graphing question (from the worksheet):\r<BR>\n" );
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document.write( "Graph: <BR>\n" );
document.write( "x+y=5<BR>\n" );
document.write( "3x-y=11\r<BR>\n" );
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document.write( "On my own, i found that the y-intercept formula for x+y=5 was y=-x+5. I also found out that the y-intercept formula for 3x-y=11 was y=3x-11. Although i'm not completely sure i'm correct, i'm quite not sure on how to graph these two equations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113044 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=113044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're correct for both. <BR>\n" );
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document.write( "Now that you have the y intercept and the slope you can plot the graph.<BR>\n" );
document.write( "The y-intercept for the first line is 5 or (0,5).<BR>\n" );
document.write( "Plot it. \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+-20%2C+20%2C+-20%2C+20%2Cgrid%28+1+%29%2Ccircle%28+0%2C+5%2C+.35+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can find another point using the slope of -1.<BR>\n" );
document.write( "That means for a positive step in x, you take an equal step in the negative direction in y.<BR>\n" );
document.write( "From (0,5) moving 1 in x, -1 in y would give you (1,4).<BR>\n" );
document.write( "If you don't want to use slope or it's cumbersome, <BR>\n" );
document.write( "another useful point to plot is the x-intercept.<BR>\n" );
document.write( "Set y=0 and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B5 ALIGN=MIDDLE  ALT=\"y=-x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-x%2B5 ALIGN=MIDDLE  ALT=\"0=-x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(5,0) Plot that too.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2Cgrid%28+1+%29%2Ccircle%285%2C0%2C.4%29%2Ccircle%28+0%2C+5%2C+.4+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then draw the line that connects those two points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-20%2C+20%2C+-20%2C20%2Cgrid%28+1+%29%2Ccircle%285%2C0%2C.4%29%2Ccircle%28+0%2C+5%2C+.4+%29%2Cgreen%28line%28+-20%2C+25%2C+20%2C+-15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Line 1 is done. <BR>\n" );
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document.write( "y=3x-11\r<BR>\n" );
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document.write( "Line 2- y intercept (0,-11)<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+-20%2C+20%2C+-20%2C20%2Cgrid%28+1+%29%2Ccircle%285%2C0%2C.4%29%2Ccircle%28+0%2C+5%2C+.4+%29%2Ccircle%280%2C-11%2C.4%29%2Cgreen%28line%28+-20%2C+25%2C+20%2C+-15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The slope is 3, so for every step in x, you take 3 steps in y.<BR>\n" );
document.write( "(0,-11)<BR>\n" );
document.write( "(1,-8)<BR>\n" );
document.write( "(2,-5)<BR>\n" );
document.write( "(3,-2)<BR>\n" );
document.write( "(4,1)<BR>\n" );
document.write( "(5,4)<BR>\n" );
document.write( "(6,7)<BR>\n" );
document.write( "(7,10)<BR>\n" );
document.write( "We have many to choose from.<BR>\n" );
document.write( "(7,10)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-20%2C+20%2C+-20%2C20%2Cgrid%28+1+%29%2Ccircle%285%2C0%2C.4%29%2Ccircle%28+0%2C+5%2C+.4+%29%2Ccircle%287%2C10%2C.4%29%2Ccircle%280%2C-11%2C.4%29%2Cgreen%28line%28+-20%2C+25%2C+20%2C+-15%29%29%29 ALIGN=MIDDLE   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+300%2C+300%2C+-20%2C+20%2C+-20%2C20%2Cgrid%28+1+%29%2Ccircle%285%2C0%2C.4%29%2Ccircle%28+0%2C+5%2C+.4+%29%2Ccircle%287%2C10%2C.4%29%2Ccircle%280%2C-11%2C.4%29%2Cblue%28line%28+-20%2C+-71%2C+20%2C+49%29%29%2Cgreen%28line%28+-20%2C+25%2C+20%2C+-15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Looks like an intersection at x=4<BR>\n" );
document.write( "Line 1 : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B5=-4%2B5=1 ALIGN=MIDDLE  ALT=\"y=-x%2B5=-4%2B5=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4,1)<BR>\n" );
document.write( "Line 2 : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-11=3%284%29-11=1 ALIGN=MIDDLE  ALT=\"y=3x-11=3%284%29-11=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4,1)<BR>\n" );
document.write( "They share a common intersection point at (4,1).<BR>\n" );
document.write( "That is the solution to system of equations. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=5%2C%0D%0A3x-y=11%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=5%2C%0D%0A3x-y=11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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