SOLUTION: The Price of a gallon of a mile was $2.20 in the year 2000. In 2003, the price had risen to $2.84. Write a linear equation relating the year with the price. Let t=0 represent the y

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The Price of a gallon of a mile was $2.20 in the year 2000. In 2003, the price had risen to $2.84. Write a linear equation relating the year with the price. Let t=0 represent the y      Log On


   

Question 1134481: The Price of a gallon of a mile was $2.20 in the year 2000. In 2003, the price had risen to $2.84. Write a linear equation relating the year with the price. Let t=0 represent the year 2000.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are given 2 points on a straight line
Plot years elapsed, +t+ on the horizontal axis
Plot price, +p+, per gallon on the vertical axis
------------------------------------
( t, p )
( 0, 2.2 )
( 3, 2.84 )
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Use the general point-slope formula:
+%28+2.84+-+p+%29+%2F+%28+3+-+t+%29+=+%28+2.84+-+2.2+%29+%2F+%28+3+-+0+%29+
++%28+2.84+-+p+%29+%2F+%28+3+-+t+%29+=+.64+%2F+3+
multiply both sides by +3%2A%28+3+-+t+%29+
+3%2A%28+2.84+-+p+%29+=+.64%2A%28+3+-+t+%29+
+8.52+-+3p+=+1.92+-+.64t+
+-3p+=+-+.64t+-+6.6+
+p+=+%28+.64%2F3+%29%2At+%2B+2.2+
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check:
( 0, 2.2 )
+2.2++=+%28+.64%2F3+%29%2A0+%2B+2.2+
+2.2+=+2.2+
( 3, 2.84 )
+2.84+=+%28+.64%2F3+%29%2A3+%2B+2.2+
+2.84+=+.64+%2B+2.2+
+2.84+=+2.84+
OK