document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692560>Question 692560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can you determine weather a graph is linear and if its a function </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427332 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=427332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you are given the graph on an x-y plane, and a vertical straight line touches more than 1 point of the graph, y is not a function of x.<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%280%29%2Cblue%28circle%28-2%2C1%2C10%29%29%2Cline%284%2C-10%2C4%2C10%29%2C%0D%0Ared%28circle%284%2C9%2C0.5%29%29%2Cred%28circle%284%2C-7%2C0.5%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you are given the graph on an x-y plane, and no vertical straight line touches more than 1 point of the graph, y is a function of x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2F5%2Bx%5E2-2x-5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2F5%2Bx%5E2-2x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you are given the graph on an x-y plane, and it is a straight line that is not vertical, y is a linear function of x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%2F2-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%2F2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you are given some sort of definition of an x-y relation, but not the graph, it is a bit more complicated.<BR>\n" );
document.write( "If more than one y is assigned to the same x, as in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y is not a function of x.<BR>\n" );
document.write( "If there is no more than one value of y assigned to each x, as in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Fx ALIGN=MIDDLE  ALT=\"y=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y is a function of x.<BR>\n" );
document.write( "If the relation can be expressed in the form <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;\" > with some constants <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y is a linear function of x. </SPAN>\n" );
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