SOLUTION: A vendor has learned that, by pricing pretzels at $1.00, sales will reach 92 pretzels per day. Raising the price to $1.50 will cause the sales to fall to 72 pretzels per day. Let y

Algebra ->  Finance -> SOLUTION: A vendor has learned that, by pricing pretzels at $1.00, sales will reach 92 pretzels per day. Raising the price to $1.50 will cause the sales to fall to 72 pretzels per day. Let y      Log On


   



Question 1084771: A vendor has learned that, by pricing pretzels at $1.00, sales will reach 92 pretzels per day. Raising the price to $1.50 will cause the sales to fall to 72 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You want to plot [ number of pretzels/day ] on the vertical axis
and [ price / pretzel ] on the horizontal axis
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You are given 2 points, which are:
( 1, 92 )
( 1.5, 72 )
Use the general point-slope formula to get the equation
+%28+y+-+72+%29+%2F+%28+x+-+1.5+%29+=+%28+92+-+72+%29+%2F+%28+1+-+1.5+%29+
+%28+y+-+72+%29+%2F+%28+x+-+1.5+%29+=+20+%2F+%28-.5+%29+
Multiply both sides by +%28-.5%29%2A%28+x+-+1.5+%29+
+%28+-.5+%29%2A%28+y+-+72+%29+=+20%2A%28+x++-+1.5+%29+
+-.5y+%2B+36+=+20x+-+30+
+-.5y+=+20x+-+66+
+y+=+-40x+%2B+132+
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check:
does it go through ( 1,92 ) ?
+y+=+-40x+%2B+132+
+92+=+-40%2A1+%2B+132+
+92+=+92+
and
does it go through ( 1.5, 72 ) ?
+72+=+-40%2A1.5+%2B+132+
+72+=+-60+%2B+132+
+72+=+72+
OK