document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966881>Question 966881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you graphed every single point of the form (2t + 3, 3-3t). For example, when t=2, we have 2t + 3 = 7 and 3-3t = -3, so (7,-3) is on the graph. Explain why the graph is a line, and find an equation whose graph is this line. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590944 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=590944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can calculate the slope using the variable of T.\r<BR>\n" );
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document.write( "let's see how you would do that>\r<BR>\n" );
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document.write( "your (x,y) point is (2T+3, 3-3T).\r<BR>\n" );
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document.write( "let (x1,y1) be equal to (2T1+3, 3-3T1).\r<BR>\n" );
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document.write( "let (x2,y2) be equal to (2T2+3, 3-3T2).\r<BR>\n" );
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document.write( "slope is equal to (y2 - y1) / (x2 - x1).\r<BR>\n" );
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document.write( "this would be equal to ( (3-3T2) - (3-3T1) ) divided by ( (2T2+3) - (2T1+3) )\r<BR>\n" );
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document.write( "simplify this equation to get:\r<BR>\n" );
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document.write( "slope = (3 - 3T2 - 3 + 3T1) divided by (2T2 + 3 - 2T1 - 3)\r<BR>\n" );
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document.write( "the 3 and the -3 in both expressions cancels out and you are left with:\r<BR>\n" );
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document.write( "slope = (-3T2 + 3T1) divided by (2T2 - 2T1)\r<BR>\n" );
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document.write( "you can factor out the common -3 in the numerator and the common 2 in the denominator to get:\r<BR>\n" );
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document.write( "slope = (-3 * (T2 - T1)) divided by (2 * (T2 - T1)).\r<BR>\n" );
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document.write( "the (T2 - T1) in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
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document.write( "slope = -3/2.\r<BR>\n" );
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document.write( "that's a common slope which indicates that the graph of the equation of the points is a straight line.\r<BR>\n" );
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document.write( "to solve for the equation of the line, take 2 points and then use the point slope form of the equation to find the slope intercept form of the equation.\\r<BR>\n" );
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document.write( "the point slope form of the equation is y - y1 = m * (x - x1)\r<BR>\n" );
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document.write( "you already know the slope because you just solved for it.\r<BR>\n" );
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document.write( "the slope if -3/2.\r<BR>\n" );
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document.write( "the point slope form of the equation becomes y - y1 = -3/2 * (x - x1).\r<BR>\n" );
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document.write( "you only need one point to finalize the pokint slope form of the equation.\r<BR>\n" );
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document.write( "you can choose any point.\r<BR>\n" );
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document.write( "let t = 0, and your point would be (3,3).\r<BR>\n" );
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document.write( "that's ecause 2*0 + 3 = 3 for the x value, and 3 - 3*0 = 3 for the y value.\r<BR>\n" );
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document.write( "you make (x1,y1) equal to (3,3) and put it in the slope intercept form of the equation.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "y - 3 = -3/2 * (x - 3)\r<BR>\n" );
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document.write( "you now want to convert this to slope intercept form of the equation.\r<BR>\n" );
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document.write( "add 3 to both sides of the equation to get y = -3/2 * (x - 3) + 3\r<BR>\n" );
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document.write( "simplify the right side of the equation to get y = -3/2 * x + 9/2 + 3.\r<BR>\n" );
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document.write( "simplify further to get y = -3/2 * x + 15/2.\r<BR>\n" );
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document.write( "that's your equation.\r<BR>\n" );
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document.write( "the graph of that eqution is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/042902.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the point (3,3) is when T = 0.\r<BR>\n" );
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document.write( "the point (0,7.5) is when T = -3/2.\r<BR>\n" );
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document.write( "the point (5,0) is when T = 1.\r<BR>\n" );
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document.write( "if the algebra for finding the slope was too intense for you, you could have found it easiwer by simply plotting several points using various random values of T and then calculating the slope several time.\r<BR>\n" );
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document.write( "you would have found that the slope was always -3/2 which indicates that you have a straight line.\r<BR>\n" );
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document.write( "the rest would then be the same to find the equation for the straight line.\r<BR>\n" );
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document.write( "                  <BR>\n" );
document.write( "  </SPAN>\n" );
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