document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=301230>Question 301230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve a question that says find the rate of change for each linear function?\r<BR>\n" );
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document.write( "Eg: The cost of cheese varies directly with the number of pounds bough. If 2 pounds cost $8.40, find the cost of 3.5 pounds.\r<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 #215982 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=215982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the direct variation formula of y = k*x\r<BR>\n" );
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document.write( "Solve for k first using the known values of x and y.\r<BR>\n" );
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document.write( "Let x = 2 and y = 8.4\r<BR>\n" );
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document.write( "Formula becomes:\r<BR>\n" );
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document.write( "8.4 = k*2\r<BR>\n" );
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document.write( "Divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "k = 4.2\r<BR>\n" );
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document.write( "k winds up being the slope of your straight line equation.\r<BR>\n" );
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document.write( "The formula for a straight line equation is y = m*x + b\r<BR>\n" );
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document.write( "m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "The slope is 4.2.\r<BR>\n" );
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document.write( "The y-intercept is found by substituting known values for x and y in the equation and solving for b.\r<BR>\n" );
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document.write( "the known values are (x,y) = (2,8.4)\r<BR>\n" );
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document.write( "Equation of y = 4.2*x + b becomes 8.4 = 4.2*2 + b which becomes 8.4 = 8.4 + b.\r<BR>\n" );
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document.write( "Solve for b to get b = 0.\r<BR>\n" );
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document.write( "Your straight line equation is y = 4.2*x\r<BR>\n" );
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document.write( "Graph this equation to get:\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-5%2C5%2C-20%2C20%2C4.2%2Ax%2C8.4%2C14.7%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-20%2C20%2C4.2%2Ax%2C8.4%2C14.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Horizontal line at y = 8.4 intersects the graph of the equation of the line at x = 2.\r<BR>\n" );
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document.write( "Horizontal line at y = 14.7 intersects the graph of the equation of the lin at x = 3.5.\r<BR>\n" );
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document.write( "This confirms the equation is good.   \r<BR>\n" );
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document.write( "When x = 2, y = 8.4\r<BR>\n" );
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document.write( "When x = 3.5, y = 14.7\r<BR>\n" );
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document.write( "The rate of change is the slope of the line which is 4.2.\r<BR>\n" );
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document.write( "This means that for every change of 1 in the value of x, y changes by 4.2.\r<BR>\n" );
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