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 8 hours of burning, a candle has a height of 2

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 8 hours of burning, a candle has a height of 2      Log On


   

Question 970261: 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 8 hours of burning, a candle has a height of 26.4 centimeters. After 26 hours of burning, its height is 22.8 centimeters. What is the height of the candle after 20 hours?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the height, +h+ on the verical axis and
hours, +t+ on the horizontal axis
You are given 2 points on the line in the format
( t , h )
( 8, 26.4 )
( 26, 22.8 )
----------------------
Find equation of the line using point-slope formula
+%28+h+-+22.8+%29+%2F+%28+t+-+26+%29+=+%28+26.4+-+22.8+%29+%2F+%28+8+-+26+%29+
+%28+h+-+22.8+%29+%2F+%28+t+-+26+%29+=+3.6+%2F+%28+-18+%29+
+%28+h+-+22.8+%29+%2F+%28+t+-+26+%29+=+-.2+
+h+-+22.8+=+-.2%2A%28+t+-+26+%29+
+h+=-+.2t+%2B+5.2+%2B+22.8+
+h+=+-.2t+%2B+28+
--------------------
Find +h+ after +20+ hrs
+h+=+-.2%2A20+%2B+28+
+h+=+24+
The height is 24 cm after 20 hrs
-------------------------------
check the equation:
does it go through ( 8, 26.4 ) ?
+h+=+-.2t+%2B+28+
+h+=+-.2%2A8+%2B+28+
+h+=+-1.6+%2B+28+
+h+=+26.4+=+26.4+
OK -you can check other point