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 10 hours of burning, a candle has a height of 20 centimeters. After 21 hours of burning, its height is 14.5 centimeters. What is the height of the candle after 18 hours?

Answer 1

Height is a linear function of time

(10,20)

(21,14.5)

slope m = (20 - 14.5)/(10-21) = -5.5/11 = -1/2

y = (-1/2)x + b

20 = (-1/2)(10) + b

20 = -5 + b

b = 25

y = (-1/2)x + 25

x=18, y = (-1/2)(18) + 25 = -9 + 25 = 16

The candle height is 16 cm after 18 hours of burning.

incidentally, (-1/2)x + 25 = 0

(-1/2)x = -25

x = 50

50 hours, the candle will be gone