document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=720148>Question 720148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.\r<BR>\n" );
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document.write( "If the relationship between cost and the number of chairs produced is linear, how do I write an equation that expresses this relationship?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441688 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=441688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it costs 2200 to manufacture 100 chairs in a day.<BR>\n" );
document.write( "it costs 4800 to manufacture 300 chairs in one day.\r<BR>\n" );
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document.write( "since there is a linear relationship, your relationship will be on a straight line.\r<BR>\n" );
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document.write( "you want to find the slope of this straight line and you want to find the y-intercept of this straight line.\r<BR>\n" );
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document.write( "to graph this relationship, you will want to show the number of chairs manufactured on the x-axis and the cost on the y-axis.\r<BR>\n" );
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document.write( "the slope of your line is equal to the formula:\r<BR>\n" );
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document.write( "slope = (y2 - y1) / (x2 - x1)\r<BR>\n" );
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document.write( "since it costs 2200 to manufacture 100 chairs, assign the value of 100 chairs to x1 and the value of 2200 dollars to y1.\r<BR>\n" );
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document.write( "since it costs 4800 to manufacture 300 chairs, assign the value of 300 chairs to x2 and the value of 4800 dollars to y2.\r<BR>\n" );
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document.write( "now you have the following values that you can use to solve for the slope.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x1 = 100<BR>\n" );
document.write( "y1 = 2200\r<BR>\n" );
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document.write( "x2 = 300<BR>\n" );
document.write( "y2 = 4800\r<BR>\n" );
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document.write( "you slope formuls of (y2 - y1) / (x2 - x1) becomes:\r<BR>\n" );
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document.write( "slope = (4800 - 2200) / (300 - 100)\r<BR>\n" );
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document.write( "this simplifies to:\r<BR>\n" );
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document.write( "slope = 2600 / 200 which simplifies further to 13 / 1 which is equal to 13.\r<BR>\n" );
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document.write( "you now have the slope of the equation of your line and all you need is the y-intercept.\r<BR>\n" );
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document.write( "this is the value of y when x is equal to 0.\r<BR>\n" );
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document.write( "to find the y-intercept, you can use the point slope form of the equation for a straight line.\r<BR>\n" );
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document.write( "the point slope form is:\r<BR>\n" );
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document.write( "y = y1 = m * (x - x1)\r<BR>\n" );
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document.write( "(x1,y1) can be any point on the line.\r<BR>\n" );
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document.write( "we'll assign the value of (100,2200) to the point (x1,y1).\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "x1 = 100<BR>\n" );
document.write( "y1 = 2200\r<BR>\n" );
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document.write( "m is equal to the slope which we have already figured out is equal to 13.\r<BR>\n" );
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document.write( "the point slope form of the equation becomes:\r<BR>\n" );
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document.write( "y - 2200 = 13 * (x - 100)\r<BR>\n" );
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document.write( "we solve this equation for y to get:\r<BR>\n" );
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document.write( "y = 13 * (x - 100) + 2200.\r<BR>\n" );
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document.write( "we simplify this equation to get:\r<BR>\n" );
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document.write( "y = 13x - 1300 + 2200.\r<BR>\n" );
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document.write( "we simplify this equation further to getr:\r<BR>\n" );
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document.write( "y = 13x + 900.\r<BR>\n" );
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document.write( "the equation i now in the slope intercept form of the equation for a straight line.\r<BR>\n" );
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document.write( "that form is y = m*x + b where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "consequently, the slope is equal to 13 and the y-intercept is equal to 900.\r<BR>\n" );
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document.write( "the y-intercept is the value of y when the value of x is equal to 0.\r<BR>\n" );
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document.write( "we can graph the equation of y = 13x + 900 as shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-150%2C350%2C-1100%2C5600%2C13%2Ax%2B900%2C2200%2C4800%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-150%2C350%2C-1100%2C5600%2C13%2Ax%2B900%2C2200%2C4800%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "y = 13x + 900\r<BR>\n" );
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document.write( "you can see from the graph that, when x = 100, y = 2200, and when x = 300, y = 4800.\r<BR>\n" );
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document.write( "this agrees with the problem statement, so the graph is accurate which means that the equation is accurate.\r<BR>\n" );
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document.write( "when x = 0, you can also see from the graph that the value of y is equal to 900.\r<BR>\n" );
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