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Question

A candle is 18 in. tall after burning for 2 hours. After 5 hours, it is 12 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 for 8 hours.

Answer 1

To write a linear equation, we can use the point-slope form:

(y-y1) = m(x-x1),

where m is the slope and (x1, y1) is a point on the line.

Let's use the information given to find the equation:

Point 1: (2, 18) - after burning for 2 hours, the candle height is 18 in.
Point 2: (5, 12) - after burning for 5 hours, the candle height is 12 in.

First, let's find the slope (m):

m = (y2 - y1)/(x2 - x1)
m = (12 - 18)/(5 - 2)
m = -6/3
m = -2

Using point 1, (2, 18), we can substitute the values into the point-slope equation:

(y - 18) = -2(x - 2)

Next, let's solve for y:

y - 18 = -2x + 4

Adding 18 to both sides:

y = -2x + 22

Therefore, the equation that models the relationship between the height h of the candle and the time t is:
h = -2t + 22.

To predict how tall the candle will be after burning for 8 hours, we can substitute in t = 8 into the equation:

h = -2(8) + 22
h = -16 + 22
h = 6.

Therefore, the candle will be 6 inches tall after burning for 8 hours.