a candle is 17 inches tall after burning for 3 hours. after 5 hours , it is 15 inches tall.write a linear equation to model the relationship between height h of the candel and time t. predict how tall the candel will be after burning 8 hourse
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To model the relationship between the height of the candle (h) and time (t), we can use the equation of a straight line in slope-intercept form, y = mx + b.
First, let's find the slope (m):
The change in height (Δh) over the change in time (Δt) is constant, so the slope represents the rate at which the candle is burning. Let's find the slope by calculating Δh/Δt using the information given:
Slope (m) = (final height - initial height) / (final time - initial time)
The initial height is 17 inches after 0 hours, and the final height is 15 inches after 5 hours.
m = (15 - 17) / (5 - 0)
m = -2 / 5
m = -0.4
Now, let's find the y-intercept (b):
At t = 3 hours, the height is 17 inches. We can substitute this into the equation and solve for b.
17 = -0.4 * 3 + b
17 = -1.2 + b
b = 17 + 1.2
b = 18.2
The equation representing the relationship between height (h) and time (t) is:
h = -0.4t + 18.2
To predict how tall the candle will be after burning 8 hours, we substitute t = 8 into the equation:
h = -0.4(8) + 18.2
h = -3.2 + 18.2
h = 15 inches
Therefore, the predicted height of the candle after burning 8 hours is 15 inches.