document.write( "Question 1176777: Solve.\r
\n" ); document.write( "\n" ); document.write( "The average value of a certain type of automobile was $14,520 in 1991 and depreciated to $6240 in 1995. Let y be the average value of the automobile in the year x, where x = 0 represents 1991. Write a linear equation that models the value of the automobile in terms of the year x. \n" ); document.write( "

Algebra.Com's Answer #804235 by ikleyn(52811) $\"\"$ $\"About$

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\n" ); document.write( "The average value of a certain type of automobile was $14,520 in 1991 and depreciated to $6240 in 1995.
\n" ); document.write( "Let y be the average value of the automobile in the year x, where x = 0 represents 1991.
\n" ); document.write( "Write a linear equation that models the value of the automobile in terms of the year x.
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document.write( "We use a linear model\r\n" );
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document.write( "    y = mx + b\r\n" );
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document.write( "for the depreciated value, starting from x = 0 at 1991.\r\n" );
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document.write( "Therefore,  y = m*0 + b = 14520  in 1991, so we just know  b= 14520.\r\n" );
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document.write( "To find m, we write\r\n" );
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document.write( "    6240 = m*4 + 14520   for the year x= 4 (1995).\r\n" );
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document.write( "From this equation, we find the slope of the linear function\r\n" );
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document.write( "    m =  = -2070.\r\n" );
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document.write( "So, the final expression for the depreciated value linear function is\r\n" );
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document.write( "    y = -2070*x + 14520,  or  y = 14520 - 2070x.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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