document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952433>Question 952433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How does the graph of y=mx+b + 4 differ from that of y=mx +b ? In what ways are the two graph similar </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581629 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=581629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "first recall that <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;\" > is the slope-intercept form of the linear equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is y-intercept \r<BR>\n" );
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document.write( "the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb+%2B+4 ALIGN=MIDDLE  ALT=\"y=mx%2Bb+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > differ from that of <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;\" > in y-intercept (the point where the line crosses the y-axis) \r<BR>\n" );
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document.write( "this one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb+%2B+4 ALIGN=MIDDLE  ALT=\"y=mx%2Bb+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > has y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B4 ALIGN=MIDDLE  ALT=\"b%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and this one <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;\" >has y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >; means that the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb+%2B+4 ALIGN=MIDDLE  ALT=\"y=mx%2Bb+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > intercept y-axis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units in higher point then the graph of <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;\" >\r<BR>\n" );
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document.write( "but, these two graphs have same slope which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that is telling us that lines are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "here is one example:\r<BR>\n" );
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document.write( "let first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb+%2B+4%7D%7D+be+%7B%7B%7By+=+4x+%2B6%2B4 ALIGN=MIDDLE  ALT=\"y=mx%2Bb+%2B+4%7D%7D+be+%7B%7B%7By+=+4x+%2B6%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4+ ALIGN=MIDDLE  ALT=\"m=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is  point (0, 10), <BR>\n" );
document.write( "let second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb+%7D%7D+be+%7B%7B%7By+=+4x+%2B6 ALIGN=MIDDLE  ALT=\"y=mx%2Bb+%7D%7D+be+%7B%7B%7By+=+4x+%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4+ ALIGN=MIDDLE  ALT=\"m=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is  point (0, 6),\r<BR>\n" );
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document.write( "now, graph them  to see that these lines are parallel, just their the y-intercept point is different \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+4x+%2B6%2C+4x+%2B10%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+4x+%2B6%2C+4x+%2B10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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