document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103141>Question 1103141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A helicopter is descending at a constant rate. In the table, t represents the number of minutes since the helicopter began its descent. The helicopter's elevation in feet at time t is represented by f(t). At what rate does the helicopter's elevation change?\r<BR>\n" );
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document.write( "t=1,3,6,10<BR>\n" );
document.write( "f(t)=6480,5740,4630,3150\r<BR>\n" );
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document.write( "A. -370 ft/mi<BR>\n" );
document.write( "B. -460 ft/mi<BR>\n" );
document.write( "C. -770 ft/mi<BR>\n" );
document.write( "D. -245 ft/mi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717814 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> at t = 1, the elevation is 6480<BR>\n" );
document.write( "at t = 3, the elevation is 5740<BR>\n" );
document.write( "at t = 6, the elevation is 4630<BR>\n" );
document.write( "at t = 3150, the elevation is 3150.\r<BR>\n" );
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document.write( "you are given that the plane descends at a constant rate.\r<BR>\n" );
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document.write( "this is equivalent to a linear rate and so a linear equation applies.\r<BR>\n" );
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document.write( "the slope intercept form of the linear equation is y = mx + b.\r<BR>\n" );
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document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "the slope is equal to (y2-y1) / (x2-x1)\r<BR>\n" );
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document.write( "x1 and x2 are randomly chosen points on the line which means they both are coordinate pairs that are calculated through the equation.\r<BR>\n" );
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document.write( "in your table, the coordinate pairs of (x,y) are equal to (time,elevation) where x represents the number of minutes since the helicopter starts its descent and y represents the elevation at that time.\r<BR>\n" );
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document.write( "we'll pick the elevation at 1 minute of the descent and the elevation at 10 minutes of the descent.\r<BR>\n" );
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document.write( "this makes (x1,y1) = (1,6480) and (x2,y2) = (10,3150.\r<BR>\n" );
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document.write( "m = the slope = (y2-y1) / (x2-x1) = (3150 - 6480) / (10 - 1) = -3330 / 9 = -370.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "to go on a bit further, the slope intercept form of the equation becomes y = -370 * x + b.\r<BR>\n" );
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document.write( "to solve for the y-intercept, we replace x and y with one of the coordinates and solve for b.\r<BR>\n" );
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document.write( "since any point on the line will do, we'll choose (6,4630).\r<BR>\n" );
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document.write( "the equation becomes 4630 = -370 * 6 + b\r<BR>\n" );
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document.write( "solve for b to get b = 6850.\r<BR>\n" );
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document.write( "the equation now becomes y = -370 * x + 6850.\r<BR>\n" );
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document.write( "when t = 0, the elevation is 6850.\r<BR>\n" );
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document.write( "this equation can now be graphed and is shown below along with the time at 0, 1, 3, 6, and 10 minutes of descent.\r<BR>\n" );
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document.write( "also shown is the amount of time that elapsed when the helicoptor lands, assuming that it continues at the same constant rate until it touches the ground.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/113001.jpg\" alt=\"$$$\"><BR>\n" );
document.write( " </SPAN>\n" );
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