A candle is 15 inches tall after burning for 3 hours. After 5 hours, it is 13 inches 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.
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To find the linear equation that models the relationship between the height of the candle (h) and the time (t) in hours, we can use the slope-intercept form of a linear equation, which is:
h = mt + b
Where m is the slope, and b is the y-intercept. We need to find the values of m and b.
We are given that the candle is 15 inches tall after burning for 3 hours. This means that the point (3, 15) lies on the line. Substituting these values into the equation, we get:
15 = 3m + b
We are also given that the candle is 13 inches tall after burning for 5 hours. This means that the point (5, 13) lies on the line. Substituting these values into the equation, we get:
13 = 5m + b
We now have a system of two equations:
15 = 3m + b
13 = 5m + b
We can solve this system of equations to find the values of m and b. Subtracting the second equation from the first equation, we get:
15 - 13 = (3m + b) - (5m + b)
2 = 3m - 5m
2 = -2m
m = -1
Substituting the value of m into the first equation, we get:
15 = 3(-1) + b
15 = -3 + b
b = 18
So the linear equation that models the relationship between the height of the candle (h) and the time (t) in hours is:
h = -t + 18
To predict how tall the candle will be after burning for 8 hours, we can substitute t = 8 into the equation:
h = -(8) + 18
h = 10
Therefore, the candle will be 10 inches tall after burning for 8 hours.