document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=789115>Question 789115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plot the equation 3x+4y=7 on the graph paper taking four points. also plot the equation y=x on the same graph paper. at what point do the two lines meet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478753 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=478753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To graph one line you only need to plot two points and connect them with a straight line. Since the problem asks for 4 points, we do the extra unnecessary work.<BR>\n" );
document.write( " <BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=7 ALIGN=MIDDLE  ALT=\"3x%2B4y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=7 ALIGN=MIDDLE  ALT=\"3x%2B4y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=7-3x ALIGN=MIDDLE  ALT=\"4y=7-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287-3x%29%2F4 ALIGN=MIDDLE  ALT=\"y=%287-3x%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so chosing random values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > we would get lots of fractions.<BR>\n" );
document.write( "However, substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >gives us<BR>\n" );
document.write( "{{y=(7-3)/4=4/4=1)}}} and we have the point (1,1).<BR>\n" );
document.write( "Increasing or decreasing x by 4 gives us other integer values for y:<BR>\n" );
document.write( "Substituting <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;\" >gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287-3%285%29%29%2F4=%287-15%29%2F4=-8%2F4=-2 ALIGN=MIDDLE  ALT=\"y=%287-3%285%29%29%2F4=%287-15%29%2F4=-8%2F4=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we have the point (5,-2).<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287-3%28-3%29%29%2F4=%287%2B9%29%2F4=16%2F4=4 ALIGN=MIDDLE  ALT=\"y=%287-3%28-3%29%29%2F4=%287%2B9%29%2F4=16%2F4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we have the point (-3,4).<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287-3%28-7%29%29%2F4=%287%2B21%29%2F4=28%2F4=7 ALIGN=MIDDLE  ALT=\"y=%287-3%28-7%29%29%2F4=%287%2B21%29%2F4=28%2F4=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we have the point (-7,7).<BR>\n" );
document.write( " <BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, nice points are easier to find:<BR>\n" );
document.write( "We could substitute a few scattered values for x,  to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (4,4),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (8,8),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (-4,-4), and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8 ALIGN=MIDDLE  ALT=\"y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8 ALIGN=MIDDLE  ALT=\"y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (-8,-8)<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2C%0D%0Agrid%281%29%2Cblue%28line%28-11%2C10%2C17%2C-11%29%29%2C%0D%0Ablue%28circle%28-7%2C7%2C0.3%29%29%2Cblue%28circle%28-3%2C4%2C0.3%29%29%2C%0D%0Ablue%28circle%281%2C1%2C0.3%29%29%2Cblue%28circle%285%2C-2%2C0.3%29%29%2C%0D%0Agreen%28circle%284%2C4%2C0.3%29%29%2Cgreen%28circle%28-4%2C-4%2C0.3%29%29%2C%0D%0Agreen%28circle%28-8%2C-8%2C0.3%29%29%2Cgreen%28circle%288%2C8%2C0.3%29%29%2C%0D%0Agreen%28line%28-10%2C-10%2C10%2C10%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The lines seem to intersect at point (1,1), so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=1%2Cy=1%29 ALIGN=MIDDLE  ALT=\"system%28x=1%2Cy=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > seems to be the solution.<BR>\n" );
document.write( "We need to verify by substituting in the original equations:<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=7 ALIGN=MIDDLE  ALT=\"3x%2B4y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A1%2B4%2A1=3%2B4=7 ALIGN=MIDDLE  ALT=\"3%2A1%2B4%2A1=3%2B4=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > checks<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=1 ALIGN=MIDDLE  ALT=\"1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > checks.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=1%2Cy=1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=1%2Cy=1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );