document.write( "Question 117170: If a function is increasing at a rate of $\"2%2F3\"$ and the points (0,2) and (3,4) are both on the graph of f(x). What will be the y value when x is 3 if the rate is changed to $\"4%2F3\"$ and the point (0,2) remains on the new line. \n" ); document.write( "

Algebra.Com's Answer #85301 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "If a function is increasing at a rate of  and the points \r\n" );
document.write( "(0,2) and (3,4) are both on the graph of f(x). What will be \r\n" );
document.write( "the y value when x is 3 if the rate is changed to  and \r\n" );
document.write( "the point (0,2) remains on the new line.\r\n" );
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document.write( "Here is what we must know in order to do the problem:\r\n" );
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document.write( "If the rate of change of a function is constant \r\n" );
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document.write( "then\r\n" );
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document.write( "#1. The function is a linear function of the form f(x) = mx + b.\r\n" );
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document.write( "and\r\n" );
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document.write( "#2. The slope m is the constant rate of change of the linear \r\n" );
document.write( "   function f(x).\r\n" );
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document.write( "and\r\n" );
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document.write( "#3. The ordered pair (0,b) is a zero of f(x) and is called the \r\n" );
document.write( "    y-intercept, as it is represented by the point on the graph \r\n" );
document.write( "    of f(x), which is a non-vertical straight line, where that \r\n" );
document.write( "    line crosses the y-axis. \r\n" );
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document.write( "Since we are told that:\r\n" );
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document.write( ">>\"...a function is increasing at a rate of 2/3...\"<<\r\n" );
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document.write( "we know by #2 above that m = \r\n" );
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document.write( "and since we are told that\r\n" );
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document.write( ">>\"...(0,2)...[IS]...on the graph of f(x)\"<<\r\n" );
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document.write( "we know by #3 above that b = 2\r\n" );
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document.write( "then by #1, we know the function is\r\n" );
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document.write( "f(x) = mx + b  or\r\n" );
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document.write( "f(x) = x + 2\r\n" );
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document.write( "So we didn't need the information that (3,4) is on the line. \r\n" );
document.write( "It was extra.\r\n" );
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document.write( ">>\"...the rate is changed to 4/3...\"<<\r\n" );
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document.write( "Now we're going to change the rate (i.e,, the slope m from \r\n" );
document.write( "to , so the new m = and since\r\n" );
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document.write( ">>\"...the point (0,2) remains on the new line...\"<<\r\n" );
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document.write( "We know that the new function, call it g(x), has b = 2, so\r\n" );
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document.write( "g(x) = mx + b\r\n" );
document.write( "g(x) = x + 2  \r\n" );
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document.write( "So we are asked:\r\n" );
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document.write( ">>\"...What will be the [NEW] y value when x is 3...\"<<\r\n" );
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document.write( "So we substitute 3 for x\r\n" );
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document.write( "g(x) = x + 2\r\n" );
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document.write( "g(3) = (3) + 2\r\n" );
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document.write( "g(3) = 4 + 2\r\n" );
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document.write( "g(3) = 6.\r\n" );
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document.write( "Since the y-value IS the function value, then the\r\n" );
document.write( "final answer is 6.\r\n" );
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document.write( "Edwin

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