document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189859>Question 189859</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131656422/algebrahomeworkh>Moving Straight Ahead</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> how do you graph time and distance on the same coordinate axes  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142453 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "First you need to decide whether time is a function of distance or distance is a function of time.  That is, do you want to see a picture of how time changes as distance changes, or how distance changes as time changes?  Typically, it is the second way.\r<BR>\n" );
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document.write( "When you say something is a function of something else, then the 'something else' is the variable on the horizontal axis.  So, given that you want distance as a function of time, then time would be measured on the horizontal (what we normally call the <i><b>x</b></i>) axis.  Distance would then be measured on the vertical or <i><b>y</b></i> axis.\r<BR>\n" );
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document.write( "The distance equals rate times time formula with which we are all so familiar is nothing more than an equation in slope-intercept form.  Usually we don't have an 'initial distance' so the <i><b>y</b></i>-intercept is zero.  But if there were an initial distance specified, that is a place other than 0 that you would be when time starts, it would be the intercept and the distance-rate-time equation would look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  d = rt + d_i\">\r<BR>\n" );
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document.write( "Which looks very much like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y = mx + b\">\r<BR>\n" );
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document.write( "Notice that <i><b>r</b></i> in the distance equation is analogous to the <i><b>m</b></i> in the slope-intercept equation?  No wonder that the slope is also known as the <i><b>rate</b></i> of change of the function.\r<BR>\n" );
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document.write( "The only difference between graphing a line such as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y = mx + b\"> and graphing something that looks like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d = rt\"> is that you need to take some special care with the scaling of the units on the axes.  For example, if you were examining what happens in a trip that lasts 3 hours at a rate of 60 mph, the distance axis would have to go from 0 to 180 while the time axis would only go from 0 to 3.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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