Application problem with a linear function: Finding a coordinate given two points

Question

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 12 hours of burning, a candle has a height of 15 centimeters. After 28 hours of burning, its height is 7 centimeters. What is the height of the candle after 22 hours?

Answer 1

In the 16 hours following the first 12 hours, the height decreased by 8 cm. Since it is given that height is a linear function, the height decreases 0.5 cm per hour. Assuming that 22 hours means 22 hours after burning started, that's 10 hours after the first 12 hours, when it had a height of 15 cm. At 0.5 cm per hour, it will shrink by 5 cm in 10 hours, so 15 - 5 = 10 cm. Because the function is linear, you could also have used the fact that 22 hours is 6 less than 28, so 6 X 0.5 = 3 cm higher than 7, and likewise the answer is 10 cm.