document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=713659>Question 713659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have forgotten how to complete problems like y=4x to graph and show work<BR>\n" );
document.write( "and y = 4x-2 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "thank you for your help i am so glad there are people like you who offer help without charging there is not too many decent people in the world anymore and it is nice to know that there are some that will help without $ being a motive but simply because they enjoy helping! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438517 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=438517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Glad to be of help.<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4x+ ALIGN=MIDDLE  ALT=\"+y+=+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4x+-+2+ ALIGN=MIDDLE  ALT=\"+y+=+4x+-+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Always look to see that the number of unknowns, <BR>\n" );
document.write( "( x and y in this case ), matches the number of <BR>\n" );
document.write( "equations. If so, then a solution is possible.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "The equations are in the slope-intercept form, which is<BR>\n" );
document.write( "ideal for graphing.<BR>\n" );
document.write( "In words, you have:<BR>\n" );
document.write( "( y unknown ) = ( slope of the line )*( x unknown ) + ( y-intercept )<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "y-intercept is where x = 0 <BR>\n" );
document.write( "x-intercept is where y = 0<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4x+ ALIGN=MIDDLE  ALT=\"+y+=+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4%2A0+ ALIGN=MIDDLE  ALT=\"+y+=+4%2A0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so y-intercept is <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;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+4x+ ALIGN=MIDDLE  ALT=\"+0+=+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so x-intercept is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means the line goes through the origin<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4x-2+ ALIGN=MIDDLE  ALT=\"+y+=+4x-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4%2A0+-+2+ ALIGN=MIDDLE  ALT=\"+y+=+4%2A0+-+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <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;\" >, so y-intercept is at <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( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+4x+-+2+ ALIGN=MIDDLE  ALT=\"+0+=+4x+-+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+=+2+ ALIGN=MIDDLE  ALT=\"+4x+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so x-intercept is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Here's the plots of the lines which shows the above data:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+4x%2C+4x-2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+4x%2C+4x-2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that the slopes are the same, so they don't<BR>\n" );
document.write( "intersect, and there can be no solution.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "There is no solution when:<BR>\n" );
document.write( "(a) The lines are parallel ( this case ), or<BR>\n" );
document.write( "(b) The equations are actually the same, as the following:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+%2B+11+ ALIGN=MIDDLE  ALT=\"+y+=+3x+%2B+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+6x+%2B+22+ ALIGN=MIDDLE  ALT=\"+2y+=+6x+%2B+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the divide the 2nd line by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you get the 1st line<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Hope all this helps. Good luck<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );