document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597567>Question 597567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> draw the graph of each of the following equations on the same graph paper<BR>\n" );
document.write( "a)y=2<BR>\n" );
document.write( "b)y=6<BR>\n" );
document.write( "c)y=2x-2<BR>\n" );
document.write( "d)y=2x-6<BR>\n" );
document.write( "do you obtain a parallelogram from these four lines?write down the coordinates of the vertices of the parallelogram </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378256 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Here is the graph of the lines. Read below the graph for the rest of the solution.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A+++++graph%28+600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2%2C+6%2C+2x-2%2C+2x-6+%29%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0A+++++graph%28+600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2%2C+6%2C+2x-2%2C+2x-6+%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a)red line: y=2<BR>\n" );
document.write( "b)green line: y=6<BR>\n" );
document.write( "c)blue line: y=2x-2<BR>\n" );
document.write( "d)purple line: y=2x-6<BR>\n" );
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document.write( "The four lines do form a parallelogram. We know that it is a parallelogram because the opposite sides are formed by lines with the same slope: y=2 and y=6 both have a slope of 0, while y=2x-2 and y=2x-6 both have a slope of 2.<BR>\n" );
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document.write( "To find the vertices of the parallelogram, find the solution for the two equations that intersect at that point. I'll use the substitution method.<BR>\n" );
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document.write( "Find the red-blue vertex:<BR>\n" );
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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-2 ALIGN=MIDDLE  ALT=\"y=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 2 for y in the second equation and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2x-2 ALIGN=MIDDLE  ALT=\"2=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=4 ALIGN=MIDDLE  ALT=\"2x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The red-blue vertex is (2,2).<BR>\n" );
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document.write( "Find the red-purple vertex:<BR>\n" );
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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-6 ALIGN=MIDDLE  ALT=\"y=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 2 for y in the second equation and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2x-6 ALIGN=MIDDLE  ALT=\"2=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=8 ALIGN=MIDDLE  ALT=\"2x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><BR>\n" );
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document.write( "The red-purple vertex is (4,2).<BR>\n" );
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document.write( "Find the green-blue vertex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-2 ALIGN=MIDDLE  ALT=\"y=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 6 for y in the second equation and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=2x-2 ALIGN=MIDDLE  ALT=\"6=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=8 ALIGN=MIDDLE  ALT=\"2x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><BR>\n" );
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document.write( "The green-blue vertex is (4,6).<BR>\n" );
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document.write( "Find the green-purple vertex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-6 ALIGN=MIDDLE  ALT=\"y=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 6 for y in the second equation and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=2x-6 ALIGN=MIDDLE  ALT=\"6=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=12 ALIGN=MIDDLE  ALT=\"2x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The green-purple vertex is (6,6).<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );