document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072915>Question 1072915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bug is moving along the line 3x + 4y = 12 with constant speed 5 units per second. The bug crosses the x-axis when t = 0 seconds. It crosses the y-axis later. When? Where is the bug when t = 2? when t = &#8722;1? when t = 1.5? What does a negative t-value mean? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687825 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x + 4y = 12<BR>\n" );
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document.write( "if y = 0, then 3x = 12 and x = 4, therefore<BR>\n" );
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document.write( "at t = 0, the bug is located at the point (4, 0)<BR>\n" );
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document.write( "if x = 0, then 4y = 12 and y = 3, the bug is located at (0, 3)<BR>\n" );
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document.write( "the distance(d) between 2 points = square root( (0-4)^2 + (3-0)^2) ) = 5<BR>\n" );
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document.write( "the distance between the x and y intercepts is 5 units and the bug travels 5 units in one second<BR>\n" );
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document.write( "the bug crosses the y axis at t = 1 second<BR>\n" );
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document.write( "at t = 2 the bug has traveled 10 units from point (4, 0)<BR>\n" );
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document.write( "10^2 = (x - 4)^2 + (y - 0)^2<BR>\n" );
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document.write( "1) 100 = x^2 -8x +16 + y^2<BR>\n" );
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document.write( "the point slope form of the line is<BR>\n" );
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document.write( "2) y = -3x/4 +3<BR>\n" );
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document.write( "use the y value from equation 2 and substitute in equation one<BR>\n" );
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document.write( "100 = x^2 -8x +16 +(-3x/4 +3)^2<BR>\n" );
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document.write( "100 = x^2 -8x +16 + 9x^2/16 -18x/4 +9<BR>\n" );
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document.write( "100 = 25x^2/16 -50x/4 +25<BR>\n" );
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document.write( "4 = x^2/16 -2x/4 +1<BR>\n" );
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document.write( "64 = x^2 -8x + 16<BR>\n" );
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document.write( "x^2 -8x -48 = 0<BR>\n" );
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document.write( "(x-12) * (x+4) = 0<BR>\n" );
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document.write( "x = 12, x = -4<BR>\n" );
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document.write( "The bug is moving up the line to the left from point (4,0) since from equation 2 we know that the line has negative slope, therefore we reject the positive value for x<BR>\n" );
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document.write( "substitute x = -4 in equation 2 to find the y value<BR>\n" );
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document.write( "y = -3(-4)/4 +3 = 6<BR>\n" );
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document.write( "at t = 2 the bug is at point (-4, 6)<BR>\n" );
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document.write( "at t = -1 the bug is located at -5 units from (4, 0)<BR>\n" );
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document.write( "3) 25 = x^2 -8x +16 + y^2<BR>\n" );
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document.write( "25 = x^2 -8x +16 +9x^2/16 -18x/4 +9<BR>\n" );
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document.write( "25 = 25x^2/16 -50x/4 +25<BR>\n" );
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document.write( "1 = x^2/16 -2x/4 +1<BR>\n" );
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document.write( "16 = x^2 -8x +16<BR>\n" );
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document.write( "x(x -8) = 0<BR>\n" );
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document.write( "x = 0 or x = 8<BR>\n" );
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document.write( "a negative value for t has the bug moving down and to the right from (4, 0), therefore we reject x = 0<BR>\n" );
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document.write( "y = -3(8)/4 +3 = -3<BR>\n" );
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document.write( "at time t = -1 the bug is at point (8, -3)<BR>\n" );
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document.write( "at time t = 1.5, the bug has moved 7.5 units<BR>\n" );
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document.write( "4) 56.25 = x^2 -8x +16 + y^2<BR>\n" );
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document.write( "56.25 = x^2 -8x +16 +9x^2/16 -18x/4 +9<BR>\n" );
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document.write( "56.25 = 25x^2/16 -50x/4 +25<BR>\n" );
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document.write( "900 = 25x^2 -200x +400<BR>\n" );
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document.write( "25x^2 -200x -500 = 0<BR>\n" );
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document.write( "x^2 -8x -20 = 0<BR>\n" );
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document.write( "(x-10) * (x+2) = 0<BR>\n" );
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document.write( "x = 10 or x = -2<BR>\n" );
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document.write( "a positive value for t means that the bug is moving up and to the left from point (4, 0), therefore we reject x = 10<BR>\n" );
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document.write( "y = -3(-2)/4 +3 = 4.5<BR>\n" );
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document.write( "at time t = 1.5, the bug is at point (-2, 4.5)<BR>\n" );
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document.write( "here is a graph of the line that the bug is traveling on<BR>\n" );
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