document.write( "Question 1144516: A company makes t-shirts and their research shows that that price and demand are related linearly:
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\n" ); document.write( "They know that in order to sell 5 shirts they need to set the price at $42, and in order to sell 10 shirts they need to set the price at $32. Find the linear equation relating price to demand. \n" ); document.write( "

Algebra.Com's Answer #765647 by ikleyn(52906) $\"\"$ $\"About$

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document.write( "Decreasing the price in 42-32 = 10 dollars increases the demand in 5 shirts, from 5 to 10.\r\n" );
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document.write( "Hence, the slope of the straight line of the demand function is   = 0.5.\r\n" );
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document.write( "Then the function itself is\r\n" );
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document.write( "    d(p) = 5 - 0.5(p - 42).   (1)\r\n" );
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document.write( "CHECK it :  at p= 42 you have  d(p) = 5.   ! Correct !\r\n" );
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document.write( "            at p= 32 you have  d(p) = 5 - 0.5*(32-42) = 5 - 0.5*(-10) = 5 + 5 = 10.   ! Correct !\r\n" );
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document.write( "You can transform the function (1) to the form\r\n" );
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document.write( "    d(p) = 5 - 0.5p + 21,   or   d(p) = 26 - 0.5p.   Thus,  m = -0.5,  b = 26.   ANSWER\r\n" );
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