A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.
To find the linear equation that models the relationship between the height of the candle (h) and the time it has been burning (t), we can use the slope-intercept form of a linear equation: y = mx + b.
The slope (m) is the rate at which the height of the candle is changing over time. We can find the slope by calculating the change in height divided by the change in time.
m = (15 - 17) / (5 - 3) = -2 / 2 = -1.
The y-intercept (b) is the height of the candle when time (t) is zero. Since the candle is 17 inches tall after burning for 3 hours, we can set b = 17 - m(3).
b = 17 - (-1)(3) = 17 + 3 = 20.
So, the linear equation that models the relationship between the height of the candle (h) and the time it has been burning (t) is:
h = -1t + 20.
To predict how tall the candle will be after burning 8 hours, we can substitute t = 8 into the equation:
h = -1(8) + 20 = -8 + 20 = 12.
Therefore, the candle will be 12 inches tall after burning for 8 hours.