SOLUTION: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 14 hours of burning, a candle has a height of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 14 hours of burning, a candle has a height of      Log On


   

Question 1148037: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 14 hours of burning, a candle has a height of 18.2 centimeters. After 31 hours of burning, its height is 14.8 centimeters. What is the height of the candle after 21 hours?
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
( 14, 18.2 )
( 31, 14.8 )
Use the general point-slope formula to get the equation
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+%28+h+-+14.8+%29+%2F+%28+t+-+31+%29+=+%28+18.2+-+14.8+%29+%2F+%28+14+-+31+%29+
+%28+h+-+14.8+%29+%2F+%28+t+-+31+%29+=+3.4+%2F+%28-17%29+
+%28+h+-+14.8+%29+%2F+%28+t+-+31+%29+=+-.2+
+h+-+14.8+=+-.2%2A%28+t+-+31+%29+
+h+-+14.8+=+-.2t+%2B+6.2+
+h+=+-.2t+%2B+21+
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Now find +h+ at the point ( 21, h )
+h+=+-.2t+%2B+21+
+h+=+-.2%2A21+%2B+21+
+h+=+-4.2+%2B+21+
+h+=+16.8+ cm
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check the equation:
( 14, 18.2 )
+h+=+-.2t+%2B+21+
+18.2+=+-.2%2A14+%2B+21+
+18.2+=+-2.8+%2B+21+
+18.2+=+18.2+
You can check the other point