SOLUTION: A manufacturer of graphing calculators has determined that 10,000 calculators per week will be sold at a price of $95 per calculator. At a price of $90, it is estimated that 12,00

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Question 1016709: A manufacturer of graphing calculators has determined that 10,000 calculators per week will be sold at a price of $95 per calculator. At a price of $90, it is estimated that 12,000 calculators will be sold.
(I) Algebraically determine the linear function that predicts the number of calculators that will be sold per week at a price of x dollars.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot price, +P+ on the vertical axis
Plot number of calculators/wk sold, +n+
where +n+ is in thousands
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You are given the points:
( 10, 95 )
( 12, 90 )
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Use the general point-slope formula
+%28+P+-+90+%29+%2F+%28+n+-+12+%29+=+%28+95+-+90+%29+%2F+%28+10+-+12+%29+
+%28+P+-+90+%29+%2F+%28+n+-+12+%29+=+5+%2F+%28-2%29+
Multiply both sides by +-2%2A%28+n+-+12+%29+
+-2P+%2B+180+=+5n+-+60+
+2P+=+-5n+%2B+240+
+P+=+-%285%2F2%29%2An+%2B+120+ answer
( change +P+ to +x+ if you like )
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check answer:
( 10,95 )
+P+=+-%285%2F2%29%2An+%2B+120+
+95+=+-%285%2F2%29%2A10+%2B+120+
+95+=+-25+%2B+120+
+95+=+95+
and
( 12,90 )
+90+=+-%285%2F2%29%2A12+%2B+120+
+90+=+-30+%2B+120+
+90+=+90+
OK